odd FTDI problem

You keep saying FTDI board, that is not what you have. You have a CP2102 based module which uses totally different drivers.
The pin labeled Reset on that module is not used, that is the reset input to the CP2102. What you can is cut the trace going to that header pin, and connect the pin to the DTR pad on the module if it has one.

I suspect the CP2102 could be connected as you describe; you may have to put the onboard ATmega16U2 into reset using its reset pin (on the other 2x3 header area near the Aref/SCL/SDA header pins).