I ended up getting a modded PC Engine and the Terraonion Super SD System 3. It also emulates the hardware using an FPGA, but allows playing downloaded files instead of just physical media. With the prices of many of the old games going for more than they cost originally, this was the only sane way to try them with original hardware at the time.
While the Analogue Duo contains an SD slot, it's only designed for firmware updating, and they specifically call out "does not play copyrighted ROM files". While I respect that decision, I think their goal of preserving gaming history would be better served allowing it. If I pay over a thousand dollars for Sapphire or Darius Alpha, I'm not going to put the game in the system and risk wear.