I have some answers for you, but they are subjective and I haven't ridden a LHT. I generally prefer a bike that steers quicker than slower, I once rode a friends Trek 520, it had heavy marathon plus tires on it and a heavy front rack, and it steered so slowly I couldnt stand it.
I was in a similar situation as you, debating bikes 26inchers, and while I never got to ride a LHT nor a Troll, when I found a used troll and ended up buying it, one of the reasons I did buy it was because as it was set up as a mtn bike when I saw it, even with 2.5in mtn bike tires, it steered nice and lightly and quickly.
While I cant give you a direct comparison with the LHT, I do feel that this aspect of the Troll, shorter wheelbase etc, gives it a more "flickable" feel vs the LHT.
I set my troll up with dropbars and have ridden it fully loaded a lot lately, and am very happy with the handling. I very very much enjoy going fast around corners, and with proper loading, it handled very very competently in downhill curvy stuff, I would even describe it as "fun" handling going down mtn descents arounds corners at 50, 60kph.
Its a real shame you cannot ride either of the bikes. Do remember though, that tire choices and all kinds of factors determine how a bike feels. I remember my first touring bike that I bought in 90 or 91 had maybe 32mm tires on it, with tread, and a bit heavy--when I changed them to 28mm slicks that were much lighter, I still recall how more nimble the bike felt, the steering was more nimble, quicker...
In this regard, my Troll has Marathon Supreme slick tires on it, 26x2, much lighter and roll better than other Marathon models, I have a lightish front rack, and the wheelset is probably a bit lighter than others as well--all of this helps with it being both lighter at the front end and contributing to how it rides and "feels".
other factors, troll vs lht, I liked the idea of being able to put wider tires on it, even with the 50mm 2in tires, I have loads and loads of room for fender setup, my fenders have a large distance between tires and fenders (I was thinking mud issues) , and also I like the possibility of adding on fork bottle racks and whatnot, not to mention the versatility of the rear dropouts (which can present issues removing the rear wheel if the fender is setup too close, not a prob for me, I can slide the wheel out of the horizontal dropouts without touching the fender)
issues of the troll--shorter frame, lower frame, ie more seat tube showing (mtn bike frame design), shorter chainstays means maybe being careful of rack choice, pannier choice, re heel strike, not a problem for me with size 9 feet.
Setting up the dropbar, I had to use a very short stem, 50mm, as Surlys in general have longer toptubes, so be aware and copy the seat to bars reach of a dropbar bike you know works for you. Not an issue at all using a short stem.
re more stable, shimmy? I did feel a slight shimmy sometimes with my troll, but I feel this was just like any other bike I have toured on, and proper, equal weight on both sides, less weight high up, solved it right away. It happened a bit when I had too much extra water/weight in the rack pack on top of my rear panniers, moved the extra water to a pannier and it was fine.
*To make this point clear, the confident handling of my troll going down mountain passes over and over again was impressive. I found myself going into corners faster and with more confidence than any touring bike I have owned.
Part of this is frame, part is probably good sturdy racks, good sturdy pannier setup with no movement, the characteristics of the 2in slick Supremes that will proper inflation have a wonderful supple ride even fully loaded that gives a really effective suspension effect (supple sidewalls) that translates into the bike behaving very consistently going around corners fast.
again, its a shame you cant ride the bikes. All I can say is that I clearly was interested in a quicker handling bike to start with, so the "truck" part of the trucker had me always leaning towards a Troll from the get go, even though I had not ridden either bike.
BUT, both bikes will make good tourers, you need to figure what aspect of their riding characteristics is more important to you. A large part of my riding pleasure is a nice steering feel, and while this is all relative, we are talking about a loaded touring bike here, they are always going to feel slow, they aint road bikes, but I will always take lighter steering over slower steering from the get go as a priority.