I just looked into different options from Europe to Doha and found that moving companies ask a lot for rather little work. I was looking at 3 cubic meters with sea fright, and waiting for 6 weeks it almost completely cost as much as your allowance. Packing myself using my own packaging materials and using UPS or something similar and receiving the things within days only costs a fraction of that. Might be different from the US, but maybe worth a check.