The cam sounds like Stage II (not surprising considering how well that design worked and how simple many of the changes were if you were making new castings), but I'm not a Stage II expert so maybe the I's and E's are backwards inside of each pair.
IIRC, on the LC2 heads, the valve arrangement is E-I-E-I-I-E or something like that. Basically you have two intake ports that sit right next to each other on each head; but on the S2 and S3 3800 heads, they are evenly spaced. That's why the LC2 intakes can't be made to work. I don't know anything about the Stage2 LC2 stuff so I can't offer any insight there.
To address, not really answer, your second statement. My main reasons would be
-1 motor mounts,
-2 4L60E doesn't enjoy a lot of popularity here and I doubt it's because of the E part,
-3 the Metric 60 bellhousing is a bit of a limitation,
-4 the limited availablity of the F-body RWD engines. The OBD2 PCM is an interesting arguement but I've used one to run my LC2 based 4.1 and it works though is in need of refinement. The major hang up there is the need for adapting the cam sensor, TPS, and IAC to work with the old hardware, electronically it works great and I can have a 4L60E that way. Interestingly enough on that subject I'm working with someone who reverse engineered a 4L80E controller to run a 4T65E to let the L67 PCM control a 4L80E.
To address what you said above:
1) Who is running stock rubber motor mounts anymore (for those who are making a lot of power)? Chances are if you are making a lot of power in an LC2 app, you've had to replace your stock rubber mounts because of their poor design not being able to hold up to the massive torque our turbo engines produce in favor of an aftermarket mount that will hold up. Sure, it is a drop-in replacement for the stock rubber mount, but it is still an aftermarket/custom part. Custom mounts can easily be made for the 3800 Series 2/3 engines so I don't think that it is AS big of an issue. I would consider bigger issues to be exhaust, wiring, and keeping your A/C functioning after the conversion is done. The Camaro/Firebird 3800 A/C compressor won't clear the crossmember in the GN/G-Body cars if left in the stock location on the 3800 engine UNLESS you modify the crossmember. I do think there's a better way, but this would involve using a different compressor and a redesign of the assy. belt drive system used on the 3800 engine.
2) The 4L60-E has FAR more support in the automotive aftermarket these days because the LSx community. I can't say it is a more supported platform than the 2004R, but it sure ranks up there. And the "E" part is what I like about it. No more problems with getting the transmission to shift WHEN you want it to in every gear (unlike governor-controlled transmissions).
3) Why is the 60 deg bellhousing a limitation? If you are referring to not being able to run a fullsize torque converter (physical size), who is running one in a "hot" LC2-2004R buildup anyway? Don't those usually get swapped out in favor of a smaller diameter, aftermarket stall converter in most custom builds already? No offense to anyone on here but I consider the BOP bellhousing to be a limitation. Transmissions that are directly compatible with that bellhousing have not been in production for years. And trying to find a GOOD 2004R that has the good GN valvebody is next to impossible (assuming you don't already have one).
4) 4L60-E's with the "60 deg" bellhousing were NOT only used in the Camaros/Firebirds. They were used in every S10 and Sonoma that came with a 2.2/2200 4cyl engine, and those were very widely produced. (They were used at least up thru 2003 model year with this "60 deg" bellhousing, possibly newer).
Again my opinions and experience. I'd consider the heads only for my application since I'm running a 4.1L block and already have to make custom headers and potentially an intake (stock LC2 works but it's not a good packaging solution) to fit the '64 Riviera engine bay.
Believe me, I wish there were a way to use 3800 Series 2/3 heads on an LC2 block. Then you guys would have another choice for better flowing heads. But like I said, the problem is going to be with the intake. And custom fabbed aluminum intakes are not cheap. I figure by the time you got an intake manifold and exhaust made to use 3800 S2/3 heads on your LC2 block, you probably could have saved some money by just getting a set of already available aftermarket heads for the LC2 which already have exhaust and intake options available as well.
-ryan