The prices you are paying ($80/hr onsite and $60 offsite) are entirely reasonable. That is simply a reasonable rate for a company if they are to stay in business. What do you think your burden rate is? I'll bet if you asked your accounting department what each employee's burden rate is you will find that you fall right in there. If you are making $20/hr that is NOT your burden rate. Your burden rate is going to be 2-3x that when you factor in operating costs. It is impossible to STAY in business and not charge those kinds of rates.
"Should I force the rate down by about $20/hr or so?" Are you kidding? What do you pay the kid next door to cut your grass?
Lowest dollars per hour often translates into a false economy. You may find someone to do the job cheaper but they may be slower or less skillful or less reliable. You have someone producing a good service for you - don't mess with it!