I have no experience with these Trek models -- but really, the issues you are describing are not at all brand-specific.

Buying a new bike in order to get disc brakes and one more cog seems like overkill, to me. Rim brakes, if well-maintained, are going to stop just fine, and a new bike won't affect the shifting that you are complaining about.

If it were me, I would get Kool Stop Salmon brake pads (in the model appropriate to your brake calipers) and slap on some fenders (if your bike doesn't have mounts, look at something like SKS Raceblades, which will still attach to the bike).

If you really want more tire clearance, then you will indeed need a new bike...But if you are riding in messy winter weather, be sure to buy one with fender mounts and put on proper fenders. That will be the single biggest thing you can do to keep the bike relatively clean and trouble-free in the slop.