I would definitely put a pressure gauge on to see what happens.
Keep in mind going uphill under load, it's constantly under boost. A L2A intercooler is good and nice but once that liquid gets hot, if the coolant flow isn't adequate, it just stays hot. I'm not a big fan of L2A myself but that seems to be pretty common with blowers. So going up hill, constantly on boost/under load, assuming a super-safe tune which probably has ignition timing pulled, it's generating tremendous heat. Since the trans cooler flows thru the radiator that's probably not helping much. Have you considered the Derale trans cooler as a supplement?
Big time things:
-canned tunes for forced induction kits are meant to be safe, nothing more. Some are decent, some are crap. It's well known in the coyote 5.0 community that whipple's factory tunes are decent but shelby's blower tunes are junk. Always get a retune.
-A proper kit will include a fuel pump if it's necessary, as well as injectors.
-Make sure the radiator isn't leaking/cracked
-Check for consumption of coolant or oil, check the oil for water, water for oil
-What was the ambient temp when climbing the hill? What was your speed?
-35's on 3.73s will generate extra load which of course generates the constant boost on the hill as well. That generates tremendous heat.
-Consider wrapping your exhaust manifold. I would high-temp paint it, then header wrap it. This will help tremendously in reducing underhood temps, especially since the header sits right under the intake manifold...just absolutely baking it.
-If you add a fuel pump, probably a good idea to add an adjustable pressure regulator.
