When I did this I moved them myself. I don’t trust hand carts and dudes stacking boxes. I just took a few boxes in the car during all of the 9 million back and forth trips.
Needles & Grooves
Corycm
bettim84
DIY
Turbo
12 years ago, I had about 500-600 when I moved 2hrs away and I did all of them myself in the car over a few trips (I was commuting between the two cities every weekend for 2 months so I stored them temporarily at a relative's first). Anyway, if at all possible, I'd do it myself (which is what I did when faced with the situation). If you can't, supervise it as much as possible.
nolalady
When I did something similar, I moved the records myself.
Crabbers
Always yourself…I did the same move last year and only I touched the boxes
djdavedk
That close, I'd say DIY also
dbarila
Ok I think I get the point now 
Mather
One day, the sun will burn out, and take with it all life on this planet. The day after that, I will still not let movers touch my records.
JohnnyCashFan
Put them in uhaul boxes, keep them out of the sun and moisture, and use your car.
dbarila
Already got U-Haul boxes coming based on previous recommendations from the forum.
kvetcha
I moved them myself. Better get a hernia belt.