First, a couple of questions to try to clarify the situation:
1) Is it the state or stake that is instructing you to clear out "Other" balances? (I'm guessing a typo, and "stake" was intended.)
2) Are these balances in a _BUDGET_ category named "Other"? Or, are they really in _OTHER_, which is an entirely separate world from budget. Funds in _BUDGET_ come from Church headquarters via the budget allowance program. Unless procedures/practices have changed since I was stake finance clerk, except for charitable donations for the humanitarian fund and similar subcategories, funds in _OTHER_ are supposed to be pass-through funds for YW camp, scout camp, and similar activities. Any money in _OTHER_ should be there for a specific purpose, and there should be a clearly defined plan/method for that money to be spent or otherwise eliminated from the account.
Now, a suggestion:
The wall to keep _OTHER_ funds out of _BUDGET_ is deliberate and should not be circumvented in a casual manner. If I were a newly called ward/branch finance clerk with such a situation, I would do do the best I could to find out where those funds came from and where they are/were supposed to go. Then, I would study the handbooks and other training materials to learn current procedures and practices. Finally, if I needed further clarification about what to do, I would ask the stake finance clerk and/or stake clerk for guidance.
Hope that helps.