Dash fits likely means its the right width. Its not going to be a bolt in swap. The amount of bracketry required is probably considerable. I highly, highly doubt that the heater box is going to fit without MAJOR rework of everything related to the heater. The biggest thing you need to understand is that a modern dash isn't just a bunch of parts you can make fit and all will be well. Vehicle's now are completely integrated from an electronics standpoint. This isn't the '80s when a cluster was just a cluster and they weren't any different between EFI and carb vehicles. Today the cluster is an integral part of the engine management. The HVAC system is also integrated into that system. There used to be one computer in a vehicle, an ECU (Engine Control Unit) or PCM (Powertrain Control Module). Today every vehicle has about a dozen computers in it, and they all talk to each other to run the vehicle. Trying to isolate one part of that is going to be difficult without an extremely good understanding of electronics. You may see some swaps done that use those parts, but they are done by big shops that have a lot of experience in such swaps. Typically what they are doing is swapping over everything (engine/trans/dash, etc. sometimes even down to the ABS and traction control). That is an arduous undertaking and is done either as a showpiece to generate business or for a customer who writes blank checks. The average guy on a project like that is going to lose steam and/or run out of money before its done.
IMO, leave the classic classic and enjoy the modern car for what it is. If you are dead set on trying this stuff I would do A LOT of research and see if there's even any resources for doing such a swap (online articles, premade harness, etc.). If not I'd just forget about it, or file it under "one day".