Removal of the dash? I don't think so.............console...yes, laying on your back (not a lot of fun) but ...............
To start with R12 is not illegal in existing systems....R12 also has much better cooling than the typical R134 replacement kits provide and will really only work to peak efficiency IF you replace /upgrade to a compressor & system that is specifically designed for R134. By the time you spend $300 for the compressor + accumulator + etc, the $40 per pound for R12 isn't so bad.....especially when R134 in a "old school" system will only cool down to about 55 degrees and R12 will easily reach 45 (measured at the duct discharge point).Mark, I'm gonna have to throw a wrench into your project. You should research the A/C discharge and re-fill before doing the job. Your system (unless already modified) uses R-12 refrigerant; which is (I believe) hugely expensive and maybe even illegal in the U.S. Nowadays, R-134 is the preferred refrigerant. Please call around to some radiator-A/C shops for confirmation; or anyone else on this site that knows and can help. This won't affect your heater core replacement, but might keep you from using the A/C.
BTW, Veronica, for someone who professes to know only 65 and 66 ponies...well done! I've been there and done that, and you got it right!
Almost forgot; Mark, do not stint when you replace the hose clamps on the core. Buy the best you can. You surely don't want to go back in there just to address a coolant leak. In fact, now would be a good time to replace the heater hoses as well. Have fun!