Moving Season

Its that dreaded time of the year. Does anyone have any advice for finding moving companies that will do trips in excess of 1k miles? My issue is that I don't have the strongest lower back so lifting heavy things is out of the question for me. The idea is that I would be hiring a moving truck to pack up my things (already boxed) and drive the truck to my destination while I drive my personal vehicle with my dog and some belongings, then have them help unload everything into my new apartment. Does that seem possible? I'll have one person traveling with me at least.

I went with the DITY/PPM because I've had coworkers unable to get their HHGs until weeks (almost a month) after reporting and I wanted to have a sense of "safety" knowing my stuff will be in a truck I'm aware of. So far I've gotten one quote that sounded like it would already break my budget (and they were asking about specific weight--which I obviously don't know until all my things are weighed). The PCS 2026 Calculator said for an E4 with no dependents and 5k lbs of stuff I would get about $6,516 from DLA, PPM, Mileage allowance, and Per Diem--which in this economy feels incredibly low.

Anyway... Any tips or suggestions?