A few observations and a little math. Please note that all measurements should be deemed to be approximate because of car-to-car differences.
The factory four speed shifter hole in '68-'69 Camaros is supposed to be (I've not personally measured this dimension, but believe it to be correct) 17.4" back from the rear of the factory bellhousing, which is itself about 6.4" deep. Using those dimensions, the center of the factory four speed shifter hole in '68-'69 Camaros is about 23.8" back from the rear of the engine. The corresponding dimensions (again, I've not personally measured, but believe them to be correct) in a '67 Camaro are 16.8" and 23.2".
The center of the shifter on a Viper T56 transmission is 20" from the bellhousing face of the transmission and an LT1 T56 bellhousing is 4.9" deep. Based on those dimensions, it appears that if you used an LT1 T56 bellhousing (which will bolt right up to a Viper T56 and a traditional SBC) and a Viper T56, the center of the shifter would be 24.9" back from the rear of the engine, placing the center of the shifter about 1.1" back from the center of the four speed shifter hole in '68-'69 Camaros and about 1.7" back from the center of the four speed shifter hole in a '67 Camaro.
A 2.66:1 first gear LT1 input shaft will swap into a Viper T56, and you could likely use an after market hydraulic throwout bearing to activate a traditional "push" style clutch.
I believe this would all work if, like the Keisler installation pictured below, you used a crossmember that kept the large portion of the T56 shifter entirely below the floor of the Camaro; that is, with only the shifter handle projecting into the car. This might raise pinion angle issues, but those could be easily corrected in most cars by the use of angled leaf spring shims or adjusting the arms in a 3 or 4 link rear.
So in summary:
Can a T56 be installed without cutting the floor of a '67-'69 Camaro? Yes, I think so.
Can it only be done using proprietary parts? I don't think so.
Please note it may also be posible to do this swap using an Aftermarket T56, whose shifter is also 20" back from the bellhousing face of the transmission, an LT1 bellhousing and an LT1 input shaft from a 2.97:1 first gear LT1 T56.
I have not personally done any of these swaps, but it certainly looks promising if you want to do this swap without cutting the floor of your Camaro.