I don't know about the CJ-1 but years ago a Turbo Commander that I was involved in maintaining had both engines HSI (hot section inspection) at the same time. No.1 had no damage but No.2 had to have a lot of rework.
This operator always started No.2 first and nearly always used batteries.
So the higher ITT due to battery start as opposed to Generator assist start almost certainly caused the damage.
If you are doing battery starts and alternating the engines then you will even out the damage to both engines, but wether this will cost less in the long run I don't know.
Hope this helps.