I was going to install lightning arrestors at the radio and ground
them to the new ground rod, is it better to place the lightning arrestors
and an additional ground rod where the coax enters the house, or will this
cause ground loop issues?

Hi Gerry, You are dealing with two different grounding issues, and I can't
comment on the ground loop one. The purpose of the lightning protection ground
is to make sure that most of the current from a strike gets to ground the way
you want. And you want it NOT to go thru your TS on its way to ground.
A ground directly at the rig can be a safety ground as well as an RF ground.
What you describe sounds like you are trying for an RF ground at the rig and a
safety ground at the entrance to the house. You may not need an RF ground, I
would concentrate on the safety aspect, and add the RF later if needed.

73 Gary N4AST