When I was learning to knurl many of the (older) books I read advised that, should the initial knurl be doubled, machine a bit off the stock and try again. In other words, alter the diameter on which the knurl is started. They never said to drive the knurl tool in deeper, perhaps because scissor knurls were uncommon in those days and the authors were concerned about overstressing the lathe bearings.
It seemed obvious to me that to get a perfect knurl, the circumference of the workpiece should be an integer multiple of the tooth spacing on the knurl wheel. The program is designed around that mathematical relationship.
Over the years I've tried both approaches, mashing and diameter adjustment, many times and my observations are:
Mashing works most of the time, especially so on softer materials.
I've never had a doubled knurl using the diameter adjustment technique.
So, use your own judgement. Try them both and decide what works best for you.