Both SD modules are fine. The blue full-size SD module is missing the voltage level translator chip but it still works. The microSD module has the level translator chip but obviously, you can't fit a full-size SD into it. That's why in my video I move all the parts from the microSD module to a custom made PCB. But you don't have to do that.
The microSD module just plugs into the 6 pin header as shown in your image.
From my tests, the full-size SD cards are faster in combination with the Arduino but that might be just because of the SD cards I personally have myself.
I have no plans to add support for more eproms or flashroms since I currently don't have much free time. But it shouldn't be all too hard to add support yourself since more often than not different chips are just slight variations of the chips already supported. The 27C801 as example seems to only differs in size, bus width and pinout compared to the 27C322. The actual programming algorithm is basically the same.