What do you mean by “it will not use up one of the USB ports on the DragonBoard 410c”? Which port should we connect it to if not to the USB type-A-connector?
Please read the 96Boards documentation here: Consumer Edition (CE) you will find that there is a 4th USB port on the High Speed Connector (Pins 51 and 53) on every board. When you design your mezzanine card, connect the FT232H data lines (or whatever bridge chip you end up with) directly to the USB pins on the High speed connector.
I had a quick read through the FT232H and the MAX2769 datasheets, I don't think that the two 4-bit parallel protocols are compatible, however this is your design and you may find a way to make it work.
I am assuming that you are laying out your own circuit board. You will not be able to hand wire this circuitry and expect it to work. The GPS signal is very small (~ -160dBm) and very sensitive to external noise sources, the USB signals are very high speed (480mbps), your circuitry will require very careful PCB design and layout in both the RF and USB sections.
Full Disclosure: I am an employee of Qualcomm Canada, any opinions I might have expressed may not reflect the opinions of my employer.