I think the 37's are part of your problem. If you have done hill climbs with them before w/o this issue, I'd say to THEN look at other issues.
A 37 DROPS your rpm by ~ 23% compared to the 30's the 2002 X might have come with.
If you started with 4.9 diffs, and went to 5.38's, that only increases rpm by ~ 9%.
So your RPM are ~ 14% lower than stock.
I assume you are using 4WD Low and not High? (Or I have an easy fix for you)
If you are running 5.38's, I am curious what diffs they are in, did you change axles/diffs too? I saw 5.13's but not 5.38's for the stock diffs....?
As you are considering a by pass on the KS, I assume you DON'T have the SC?
Other than that, I agree about checking the fuel and air filters and the MAF (Use MAF cleaner, the other stuff tends to leave residues and mess it up worse, etc), the exhaust/muffler can have an internal obstruction (Rust flake clog, etc), and would add doing a code read to see if the ECU is storing any useful info.
Your wires, plugs and distributor can also be messing with you....especially if its triggering a fail soft condition. The same goes for the battery/plethora of ground straps, etc...if there's a loose battery connection or loose/corroded stap, etc, as you climb, the continuity of the ground path, etc, can be lost, and trigger fail softs/not send sparks as well, etc.
