Am I likely damaging anything by not minding the pain as much as I could
In my unfortunate experience, its possible. And some of that pain could be a pretty constant reminder.
I myself would not cheap out on the movers--having moved many times, it was so incredibly worth it to have other people do it the last time I moved.
Just get written stuff on bonded and insured. I had the most uncompensated damage using movers. Me packing? A pain but awesome on the survivability because I was ... careful. And used 50+ lbs of wrapping paper.