You can go down to a 24 on your RSX crankset. That shouldn't pose too much of a challenge to an LX rear derailleur unless you shift to the small-to-small combo.
If it were me, I would consider getting some beefy top-quality 7075-alloy chainrings instead of the stamped-steel RSX rings, while you're at it. Real Design makes some awesome ones, as well as RaceFace. Avoid the 6061 models and go for the hard, gouge-resistant, long-wearing 7075 versions. I see some on sale here
for $70 for the RaceFace 24-34-46 set in the 74/110mm pattern that you need (get the black ones, not the unramped silver ones).
One thing about the RSX shifters, too... the front shifter doesn't have the trimmability of most STI shifters, or not the ones I've used anyway. They rely on the chainrings' shift ramps to help them get the granny-to-middle upshift, in particular, so you need rings with shift ramps/pins. If you go on long tours then it might be worth thinking about some bar-end shifters, which have a fail-safe friction mode to fall back on (and friction front shifting all the time).
There are 8-speed cassettes that have an 11-34T setup, too. The last jump is pretty dramatic (from a 26 to a 34), so it's not that great of a solution, but it was worth a mention I guess.
Anyway, that's my 2c, hope it is food for thought