Definitely sounds like an encoder/rail issue. The way the stitch regulator works, you need uniform rolling of encoder wheels on the carriage and the frame tracks (no spots where they slide instead of roll).
Large stitches indicates the carriage or machine is sliding instead of rolling in spots - if the wheels aren't turning, the encoder doesn't think the machine moved. That could be issues with the rails on the frame or carriage or it could be the encoder wheels.