I have just learned that to rechamber a 416 Remington Mag to a 416 RUM, the reamer needs an extra long pilot so that cutting does not start before the pilot is secure in the bore.
This pilot will be over 2 inches long, so I am wondering where it goes as the cutting proceeds.

Can it damage the rifling? Does it turn with the cutter, or does the cutter turn around it?

Is there an easier way to improve chambers?

First off, running an Ultra Mag reamer into the 416 Rem will not improve it. Quite the opposite in fact! It will,however, make it bigger! The risk ,if the pilot does not engage, is that the reamer may begin to chatter. With a good setup and reasonable care this won't happen. A reamer with a long pilot would simply run on up the bore. Again, with care, it should do no harm.
In rechambering a 30/06 to one of the 300 magnums the pilot doesn't engage right away either. I have lost count of the number of these I've done and never had a problem. Regards, Bill.

Bill -

Thanks for the reply...I just need a very good gunsmith.

I also appreciate the distinction you make between "improved" and "bigger".