There are systems that are just what you want, and they come from... er, Analogue. Specifically the Analogue Super NT (FPGA SNES clone) and Mega SG (Genesis clone). They're a little pricey and they need original carts, but they come closer to the real thing than any software emulator I know of, with almost zero lag too.
Highly recommend the misterfpga, I sold my nt mini noir after getting it, so much better and less half based (for example nt mini noir's jailbreak had Genesis support but no controller remapping making it useless with the 8 bitdo genesis controller).
Also very impressive to see all the work being done on mister cores including things like Amiga, Acorn Archimedes, the first Playstation and Saturn
Mister also, just works. But yes, it's really not beautiful (in terms of living room aesthetics). I'm not being facetious, but Mister is really cheap and easy to get running and as I always say, the community is amazing. One of the best internet communities around IMO.