Many people here have done this and the last time it was asked a few gave specific shippers they had good experiences with. Give the thread a few days and I'm sure they'll speak up, of spend some time searching.
I helped Glider (username) ship hers across the country and it went well. You could try her but I don't know how active she is here these days.
There are good shippers out there but certainly hard to find in a sea of shady ones.
Try Chris Ridgeway (Ridge here) or MSD.