Aw, I was totally MacGyvering a solution for you with the 3-in-1.
By using the FCSR DLDI interface you can embed a FAT volume inside a .nds file. That would let you put the 3in1 Expansion Pack Tool on the 3-in-1 with some GBA roms packed into it, and from there you could run the games in PSRAM mode.
The problem would be the saves. FCSR is read only so saves wouldn't get backed up, and the save in SRAM would be overwritten with blank data each time you loaded a game. To get around this, you would leverage a flaw in the EZ4 Client.
The EZ4 Client forces GBA games to put their save data in the wrong part of the SRAM when you run them in PSRAM mode. This means that you could play one game at a time and be able to save properly, but only until you switch games, at which point the save would be overwritten by the new game. Not ideal, but it's better than not being able to save at all.
I have no idea if it would really work, but I thought it was a pretty clever idea.