Come to find out, the issue with the floppy is not the floppy at all. The system will refuse to boot ProDOS whenever there are two storage devices. I have a total of three storage devices, LPC ROM, HDT file located on a PC using a serial port, and the floppy. I have been using the LPC disk for booting. I tried a test, I booted using the LPC drive and I disabled the floppy. But the PC was connected and the ROM for the serial port was present. It failed to boot just like with the floppy. I then booby trapped the ROM for the serial port to see if any code was executed, and it was not.
I have been unable to fix the booting issue with the floppy. When the floppy ROM is loaded, ProDOS refuses to boot. Without the ROM, ProDOS happily boots from the LPC ROM all the way into the BASIC Interpreter. From there I am able to copy files from the ROM drive to the /RAM drive in the second 64K memory bank. The 80 column text screen works perfectly also. Both of these features require the use of the memory switches, so I believe everything is working correctly. Because of these successes, I convinced myself the issue was related to the floppy emulation.