The suggestions for low(er) gearing, I think, are spot-on, unless you are comfortable doing loaded climbs with the gearing that you already have. I know that I love me some low, low gears.
I'll throw out another suggestion, which for me makes loaded climbing and almost all facets of touring more comfortable: aero bars.
It is a costly modification, as your LHT probably has a 26.0mm stem/bar clamp, and aero bars are designed to be used with 31.8mm stem/bar clamps, which means that in addition to purchasing the aero bars, you will be replacing your stem and handlebars. The possible upside to this is that if you do have any issues with your current stem/bar combo they can be rectified at this time (Shorter/longer stem? Riser stem? Wider/narrower bars? Bars with a shape different from your current bars? Different/thicker/thinner bar tape?).
Zipp Speed Weaponry (ugh…), part of the SRAM group, makes aero bars and aero bar accessories that allow for a wide range of fitting solutions. The aero bar setup on my touring bike, based upon their Vuka Alumina bars, bears little resemblance to the aero bar setup that you see on a time trial or triathlon bike. The elbow pads are much further aft, they are spread apart (Zipp sells an accessory called "Wings" to facilitate this) and the whole contraption is about 2" above the height of handlebars themselves by using what Zipp calls "Risers".
This modification, in its entirety, will cost hundreds of dollars. I don't know if you are interested in something quite so spendy. It also requires time, as there are many small adjustments to be made that can affect your level of comfort, and the only way to figure this out (at least for me) was through trial and error: having the necessary wrenches easily accessible while doing training/regular non-touring rides and making these adjustments. Once dialed in, though, the comfort offered by the aero bars is for me more than worth both the monetary investment and the weight penalty that they impose. They also provide a nice place to mount a computer or GPS (or both), as well as a place to hang a hat, helmet, or any wet clothes that need to be dried while riding.
I should also mention that adding aero bars might have you repositioning your saddle very slightly. I can't say what this repositioning process might entail, but it could mean raising or lowering the saddle, changing the tilt of the saddle, or possibly sliding the saddle either forward or rearward along its rails. Should you choose not to run aero bars, messing around with your saddle positioning might not be the worst thing to do anyway.
Best of luck, and enjoy your ride!