I am combining two 8 ohm full range drivers of similar frequency response, but slightly different RMS ratings in parallel. They will be together in a shared 1 cubic foot enclosure (I can seal them off from each other if that’s strongly recommended…but I basically added their recommended individual sealed sizes)
Are you planning to use an 8" and a 4" driver in parallel? Surely not? Assuming your 2 bass drivers are similar and housed in such a small enclosure, have you considered an isobaric design? This design will kid the front speaker (the one you can see) into thinking it's in a much larger enclosure and it will deliver far better and deeper bass, if well implemented.
Or have I misread and you intend to use these 2 drivers as full-range devices with no crossover? This would be most unconventional and your treble would be poor as you have no tweeter as such. Also the small speaker would no be protected from the bass frequencies.
Regarding an amplifier, I'd suggest one that includes a "room correction DSP" feature as this processor has no idea of where the peaks and troughs are generated. It merely measures what the microphone picks up at the listening position and does its best to adjust the frequency response to compensate for these peaks and troughs, whether caused by the room or the speakers. In the case of a DIY speaker, where you are not building dozens of prototypes to judge and compare (as brands do), DSP should do good.
I think we need to know more about your ideas regarding crossovers, cabinet design, etc.
PS - Although very old and out of print, there are 3 great books written by G A Briggs, the founder of Wharfedale, that go into DIY speaker theory and practice in a very understandable way. Accepting their age, you may find useful information there. His books are Loudspeakers, More About Loudspeakers and Cabinet Handbook. I found the last one the most helpful when I was building my own speakers in my mis-spent youth! Copies likely available from Amazon, Abe Books and other used book sites. Good luck.