Mycoalson, Expense wise keep everything in perspective, the bike comes second to most other life items.

I think you may need a new chain. Pins on a new chain will align with a 12" span. An extra 1/16" indicates a stretched chain which seldom works properly with a new cassette/freewheel. Measure at three points of the chain. KMC and SRAM have perfectly good inexpensive chains.

Brad