Actual, overnight, long distance rides are relatively rare on my LHT, but not unheard of. Most of the miles come from riding around town and commuting. The bike is neither fast nor light, but then neither am I, so it might not be the bike's fault.

It has occurred to me that probably 75% of my riding has me carrying only a trunk bag or less, which means a full touring bike is probably overkill. But then when going through the mental exercise of selecting a faster bike, I find myself thinking about how much I like the fact that if I unexpectedly need to load up the bike due to an unplanned stop at the grocery or find that I need to bring a lot of extra stuff home from work, I'm suddenly on the right bike for the job. It's not like the bike is unpleasant the 75% of the time that it's only moderately loaded, far from it. It's just not particularly fast or light. I've decided that having a bike that I can load up without thinking twice about it and that is comfortable for long rides, is far more preferable to me than one that is fast and light. However if I never took the bike on any overnight tours, and the only loads I carried were those occasional shopping trips, I would probably go with something a little zippier. But for how I do ride and how I use it, I'm very happy with the LHT as my daily ride.

As you've already said that wheels can be a problem for you, then I'd echo what's already been said: wider, high-spoke wheels are going to be your friend. That does mean that many lighter, high speed bikes may not be the best fit. But my guess is that if you can find a bike that will take a tire of a suitable width, it will be otherwise fine with a heavier rider. If speed is your goal, figure out the wheels you want, then select from the bikes that can handle those tires one that is built most for speed. As a heavier rider myself, and one who tends to carry extra weight besides, I find the wheels to be the weak point, and I wouldn't make any sacrifices there for the sake of speed, but within the limits of a wider, stronger wheel, I think you'll still find zippier options then a full touring bike, if that's your goal. It's not mine. After considering a 2nd bike for when I don't need the full touring set up, I decided what I'd really like as a 2nd bike is a fat tire bike. No speed gains there either. I guess I'm destined to be slow no matter what, and I'm okay with that.