Can an H-bridge drive another bridge?
Can I use these two TX output pins to drive an H-bridge - or another
full bridge?


Yes. According to AN98080 page 16,

&quot;For long range systems, external power MOSFET-transistor pairs can be
connected to TX1 and TX2 to allow for even higher currents.&quot;



Will increasing the voltage help with the transmission range?


Yes, but increasing the current can also help. With a higher current driver you could reduce the number of turns to reduce inductance and increase inductor current, producing a stronger field. Page 17 of the app note says:-

&quot;La ≤ 800 μH when operating the HTRC110 in normal
mode at I antmax = 200 mA and La ≤ 400 μH for the burst mode at
I antmax = 400 mA respectively. If using an external antenna current
boost stage, even lower inductances are required.&quot;

Provided the 5 V power supply can handle it, increasing current will be easier because you can drive the external MOSFETs directly without needing level translators. Ultimately you are limited by the coil needing at least 1 turn. If you can't get enough field strength with that then you need to raise the voltage.


If this approach won't work, how else might I increase the range? A
different IC? Etc.


If this doesn't work it's either because you are doing it wrong (not tuning for resonance, wrong Q, wrong coil dimensions, too many turns) or you are just expecting too much. You can always increase the field strength to get enough power to activate the tag, but if it's not close enough to significantly influence the transmitting amplitude it won't be detected. For longer range you may have to look at a different technique.