For gain, have a look at MMICs. Minicircuits sell them in kits that
give you a good range of performance. They're easy to use, and run on
a single supply.

I think the idea of using the LVDS inputs on the FPGA is a good one, if
you can get that into the clock lines you need to use. Otherwise, you
only need a little gain to get to levels you need for logic input. Do
your clock input lines have a bit of hysterisis? Do they have high
enough input impedance to be used with a step-up transformer? Can you
reliably bias the transformer DC return to a point between the
hysterisis trip-points. I suspect you can do a better job with your
logic-gate amplifier, too. Or you could make a fancier input using one
of the very fast comparators.

Cheers,
Tom