I think I will break with the norm. it sounds like you want a LHT just buy one. They are great touring bikes, commuters, and good casual riders. older kona sutras(what I have) also great, trek 520 also worth a look.
I would get a touring bike I would not even consider a road bike, skip the $2k 1x LHT get one with a triple(personally I would get a disk trucker). Used market might be pretty weak right now and over priced. seems like you are already kinda looking at 1-2k range there are new options in that range.
If for some reason you have a shoe string budget the "90's MTB" is a OK option just make sure it has a way to mount the racks. I would just keep in mind MTB's and hybrids while they will work it usually requires more from the end user.