When an account is transferred, the payments in the previous ward do not get transferred to the new ward. Instead, there is an effective date for the transfer. If the effective date is in the past, then CHQ will credit the previous ward for any charges already made to them after the effective date and charge the new ward instead. If the effective date is in the future then CHQ will continue to charge the previous ward until the effective date and then start charging the new ward. By choosing the correct effective date the previous ward should be left with a zero balance (the remaining charges and the payments from the missionary balance out) and the new ward should also start with a zero balance (there are other considerations if the family/missionary is behind on their payments but I'm assuming here that they were up-to-date).
It sounds like when the financial responsibility was transferred the effective date was set as the beginning of his mission. That's the only way I can see that you would end up with such a large negative balance.
At this point there are two things that could be done. First, after checking with the previous ward and verifying the situation, you or your bishop can call again and ask CHQ to change the effective date. That would reverse the charges to your ward and put them back on the previous ward. Alternatively, the previous ward can write a check from the missionary's account in their ward (which should have a positive balance now) and send it to your ward.