The part about "The engine was built 3 or so years ago and has just been cranked up on occasion during the car restore." might be a problem. Did a good cam break-in take place? I'll describe it below in some detail.
The other thing bothering me is that startups after sitting awhile can possibly have some moments of low oil pressure; the Chevy oil pump is fully excellent, but there are a bunch of places for that oil to go before pressure builds! Sometimes people start an engine and go vroom! vroom! with it before pressure is everywhere. This is hard on things. There must be oil to keep the opposing bearing surfaces from actually meeting; they are designed to run with a film of oil between them, because oil cannot and will not collapse under pressure (that's why hydraulics work). [This is why I went to synthetic, but... read on; this turned out to be a really severe error for breaking in an engine, and cost me a lot.]
Sometimes you do lose a cam when breaking it in, yes. The most frightening scenario is when you have to replace a lifter with a new one; that'll kill a cam lobe lots of times. If you lose a lifter, I would strongly recommend changing the cam. Besides, if you lose a lifter, you need to find out *why*. Was it junk in the oil system? Sometimes just the crud on shop rags will do it. I would recommend a very close, and I mean, magnifying glass inspection of the cam and each lifter. Make darn sure the lifters are kept in order so you can see what lifter did what. (The pros have a board that holds the lifters, because they know a lifter cannot be put into a different spot and work.)
Your lift values are a bit more than I'm used to in a small block, but Comp Cams does good cams. I looked and see .47 lift, 270 duration. But the problem is different places measure cams differently. One place will measure when the cam has just barely taken up the slack in the valve train, another will measure when the valve is effectively open..
Hmmm, did they put extra heavy springs into your heads?
I lost 2 cams in rapid succession not long ago at all. The answer was quite strange. On my big block 454, the factory cam had an oil slot all the way around the middle of the rearmost load-bearing surface. This created a path for oil to get from the bottom hole to the top hole, and thus to the other bearings. Without that slot, which isn't on any other cam, oil didn't get to the other bearings! Cams died.
Now, my databook says that this was only done on "early 427 L-88's (1965-67)". I bought this 454 LS-6 in the crate about 1988 or so (before Chevy started confusing everyone by re-using "LS-6" on another engine).
The cams my mechanic put in did not have that oil slot. The lobes went flat. We finally figured it out. We could not find a cam with that slot anywhere; in fact, the cam companies said, "You have WHAT? I've never heard of that!". Finally, we just got the block machined to not need that slot to get good oil flow to the cam bearings. Then it was compatible with all those big-block cams out there.
I still don't know how I ended up with an early block and cam. I can only speculate that Chevrolet made a bunch of big blocks without that extra oil drilling, and perhaps Chevy had a bunch of slotted cams to get rid of. It was definitely a 454 LS-6 in the crate, though, not a 427 L-88.
Generally the cam manufacturer gives you some very special grease & lubricant to put on the cam lobes and on the bottom of the lifters.
When it gets time to break in the cam, there is a set procedure. It's something like this, and different mechanics do it differently, generally on a "Here's what works for me" principle; it's a little bit of an art.
Prime the oil system the day you fire it up: Pull the distributor. You should use the metal part of a flat blade screwdriver in an electric drill, put it down the distributor hole to the oil pump, to thoroughly "prime" the oil pump so there's oil everywhere in the oil channels at the moment of startup. Doesn't hurt to see the oil actually coming out, either. Put the distributor back in.
Static time the engine so it'll catch immediately. Bring the engine (by hand) slowly around to cylinder #1. Before you reach #1, on a previous cylinder, put a piece of paper between the points of the distributor. Now, pull it towards TDC. The distributor should be roughly pointing at #1 (you've marked this or know it, right?), and the "timing light" slot on the harmonic balancer is also coming on to TDC. When the balancer is on TDC, very gently turn the distributor towards the rotation until you can pull the paper away; that's top-dead-center-setup ignition (see, when the points open, the coil fires). Tighten the distributor to "not final but good enough for now". You should do final timing with a timing gun to the specs for your engine after the cam is broken in.
Now attach a tachometer to the distributor; if you're running a souped-up ignition, attach it to the wire that's given for attaching tachs. Note: make darn sure the tach wires aren't anywhere they'll burn through (exhaust manifolds are particularly bad ... *grin*, imagine how I know this) and that you can see them from where you adjust the carb for engine idle speed. (For fuel injection, you may have to start and do speed from inside the car, if you don't have a tach, put the tach on the widshield, etc.)
The carb should also have gasoline in its float bowls and also be "ready to rock"; it isn't that much work to make sure the fuel line down to the fuel pump is full, too.
What you're trying to do is make sure that *nothing* interrupts the engine running for 30 minutes or so.
Think about: Will this engine overheat? You're going to be running it hard with no air blowing, like it's in heavy traffic. You may want to get one of those big fans and aim it at the radiator. Is the cooling system full and "burped" free of air? When the engine first is running, you may need to add fluid as the air comes out of it. (Don't do this when the engine is hot, or you'll get a face full of angry steam and coolant).
When the engine is fired up, it should be taken straight up to 2000-2500 RPM, and I mean STRAIGHT UP. This means use the tachometer in the engine compartment / windshield. Some people use the idle screw on the carb to hold this RPM; that works too. I used another tach, and found out the tach in my Camaro reads 1,000 RPM **LOW** at 4,000 RPM; e.g., 4,000 RPM indicated was 5,000 true RPM, and with a 454 big block, that's getting into yellow to red line territory.
If you have to sit in the driver's chair and hold the RPM, then do it, but this is not recommended. You want to be watching the engine, looking for leaks *especially* (with all those new gaskets, this is when it's gonna leak!). Some people vary the RPM a bit between 2,000 and 2,500.
After 30 minutes most people shut the engine down. Then while it's warm and the oil is nice and runny, they drain the oil, now full of little bits of "stuff", out. They also remove the oil filter, also full of little bits. They put in new oil and filter.
Then they tend to go around the engine with a torque wrench and see if any bolts feel strange. A "stretchy" bolt, say, that should tighten to 50 ft. lbs, but easily tightens to 45 for a full spin, is stretching way too far, and will snap off if you push it. The ft-lbs spec is actually the desired stretch spec from the mechanical engineers who designed the engine. You need a new bolt of the desired strength. You'll have to swap it out.
Please don't make the same mistake I made! I put in synthetic oil to break in the engine. Hello, scuff marks in the cylinders! Hello, scuffing on the cam, main, and connecting rod bearings! DO NOT DO THIS ! If you want to run synthetic, wait until the engine is broken in. My engine had to come out and all the bearings had to be replaced. Oh, joy. Imagine how happy I was. How thin my wallet. Now it's running 30W oil.
I hope some of this I'm passing along will help. If only the Don't Break In On Synthetic part, it'll have been worth it.
Take care,
Dave