I need to change the tuning machines on my Gibson Les Paul Special SL. I want to avoid filling/drilling new holes, so I bought the Historic Spec Gibson tuners. The holes line up, but I encountered a different problem. The bushings are "push-in", and the ones that came on my guitar originally were the screw type. This wouldn't normally be a problem, but the small washer that sits on the headstock under the lip of the bushing is too small to fit the new, push-in bushing.

So, would I be able to just find the right size washer and use them, or is there a set of tuning machines that actually matches the originals? Thanks.