I may have screwed up but I was told by a guy I trusted (mechanic) that to store my heads while I am in the process of building my 327, I should coat them in axle grease, I did one and it just didn't look right. Did I just screw it up?

No but did you coat the important parts, valve seats and guides, 2.02 are rare on a 67,

Grease and then wrap in kitchen grease proof paper
Which is basically how parts...cams heads lifters, bearings where stored, even brought over the counter many years ago before plastic sealing , blister packs etc.
I still have some of these original items for our vintage cars packed like that, from the manufacture.

Well this is good to see that I didn't mess it up. Now I will go ahead and do the other. John I coated what I could, forced some in-between the springs, is there something I may not be seeing, should I disassemble and coat? Steptoe I greased it all up and placed in a plastic garbage bag and wrapped it up. Thanks for your comments guys.

I would pop the valve collets off, pull valves out a little, smear valve stems, seats faces, slide valves back up....and wire across the top of the springs, leaving the collets off.
So when come to re use u can wipe off excess in the ports etc, check valve/ seat surfaces.. pop the collets on and good to go...
Having valves hard up on seats like that fro long periods is not a good idea.

I would just use WD-40.

+1

+2 and wrap in a plastic trash bag

Grease is a nightmare to remove

We have used WD40 and other alternatives but if stored for long periods the stuff eventually creeps down off the parts.
There are some marine based lanoline products that maybe better... but rather than risk having non replaceable vintage parts go bad, having tried them.... thu they work well on the boat trailer fishing gear etc

AS to cleaning grease off... its no biggie....wipe any excess and if it is a 'must do' hit with degreaser and hose that off.

OH and as a side note, because of now having the boat, saltwater fishing several times a month all yr round, trailer/ engine maintenance etc, I now use Evenrude marine greases for everything