OK. We have a lot in common. I was a assembly language programmer using an Intel development system for the 8080. I also did some CP/M programming just because the CP/M based computers were a fraction of the cost of an Intel ISIS II workstation. The CP/M type computers were used in proses control and material testing. What we put out on the floor of the manufacturing area were actual ROM based microcomputers with a in-house integer BASIC interpreter we did. The I/.O system was designed by the engineers and we had to use assembly language to read and write the ports of the 8080 CPU. Very primitive by today's standards.
A modern Intel based PV operating system s are based on the 386 architecture not the 8086 used in early IBM PCs. Starting with window 95, you could get to I.O ports as virtual devices, but I have no deference on that at hand.
The early MS-DOS PCs you used were programmed within the limitations of the 8086 architecture. Which simply meant that if you tried to read from port 3F8 (hex) you had to have a real piecse of hardware wired to decode that literal address. The I/O cards would have little DIP switches that let your re-wire the address decoder to respond to another address. That would let you add more serial ports to the system.
With the i386 you have many extensions to the old 8086 code. Notably, the ability to run in a virtual mode instead of the real mode. So instead of setting a DIP switch, just tell the software to make exceptions to some I/O address. Any reference to 3F8 would map to 2F8 instead. (OK, that is over simplified, but has the idea.)
Your USB device should map to the four standard ports, COM ports 1,2,3 and 4. A higher address means some other program has already taken over the lower ports. Or there are lower physical ports in the system.
The above is a port serial port PCI card. It can literally be four ports. You can, if needed, disable some ports.
But a USB port is a different thing. It has to emulate a physical serial port using a driver written in i386 code to let older programs use the addresses scheme of a physical port.
I still have trouble visualizing how you have things connected. You have only one USB adapter, - Right? It should map itself to the first four COM ports. Any real COM ports should be disabled in BIOS.
Time for bed. More tomorrow.