When trying to do this, it's hard to keep everyone on the same page. I would make a series of transactions resulting in the desired effect; no taxation with a loan in the new plan.
1) Directly roll over the cash into the plan of the new employer and offset the loan. Let's say you roll over $10,000 and offset a $5,000 loan.
2) Immediately take a loan from the new plan; $5,000.
3) Roll the $5,000 over, since you have a 60 day period to roll over the loan offset from the previous distribution.
This will only work if you have enough in the cash rollover to secure a loan in the amount needed to cover the original offset. If it can be done, you'd acheive the desired result without getting all the other parties involved.
Good Luck!