Define your problem a bit more. Are you just harvesting some expensive or hard to get devices, or is your board failed and you want to reflow the old chips to make your board work again? Re-Balling of a chip with that many pads will probably be a waste of time at best. As Rocky used to say to Bullwinkle "That trick never works". Successful removal, re-balling and crude failure rate when reflowing the parts is probably money wasted unless the parts are valued at over $500.00 each. I have been down this road with contract manufacturers and financially the outcome is never positive nor is the reliability after 6 hard hot/cold thermal cycles in the chamber!! You end up shipping questionable junk to your customers and getting bitten in the ass (or fired) six months down the road of field failures when I stand in front of the engineering group and say "I told you this was a bad idea". Your only real option, and it'll cost, is to contact local 'board house' contract manufactures who are specialized in surface mount techniques. Anything less is 'less'.