Welcome to FT, Tina.

Just call the awards desk of each program to find what your options are (taking notes, of course). Hopefully each programs will have available for award at least one FC seat for a flight in common with the other... Generally, you will be able to make and hold a reservation for some time before having to ticket it (72 hrs for UA, don't know about US), so that gives you a bit of time to get it all together.

It's like putting together a puzzle. Can't think of any other alternatives.

Edited to add that flights on UA to LAS do not have F (it's TED ), though you could route thru SFO/LAX and at least get F in that segment...