I would (re)load 38 Special brass (if it fits the chamber length,,or trim it down to 38 Long Colt length which is likely the proper length for the orig caliber.
Then load 'Mid Range Target' loads using cast or swaged 148gr Hollow Base Wad Cutter bullets.
These are standard .357d but the soft lead and hollow base will expand upon firing and engage the rifling of the 360 bore size no matter what it happens to be at this point.
It's a common load used by shooters with S&W Victory revolvers rechambered to 38Special but still having the 38S&W bore bbl on the gun with their slightly oversize (for 38Spec) bullet barrel.
You can try 38S&W cartridge in the chamber and see if it will chamber...they are loaded with a lead bullet that is likely just right for the 360 Rook at .361/.362d.
The old Brit Military 38S&W load was a 200gr bullet (38/200) meant to do everything the heavy .455 Webley was capable of doing. But that's another story.
The 38S&W case is slightlylarger in dia than the 38Special/38 Colt, so it might not chamber,,but it's worth a try.
If it doesn't,,then I'd simply go to the load above and see what kind of results you can get.
The Mid Range TArget Load (3.5gr Bullseye/ 148gr HBWC Lead) was and still is a standard Bullseye target pistol load in competition and used at 50and 25 yds to shoot 1" groups.
In a light weight Rook Rifle I would welcome a cartridge that would do that and not knock the snot out of me.
Easy to load,,brass all over the place as well as bullets and powder choices.
A 25-35WCF would not be too pleasent to shoot more than a few rounds in a light weight Rook.
The 25-20,32-20 and others in that range would be fine but would take work & $ to do a conversion.
I'd at least try the 38 Special/148gr WC bullet angle first and see where it goes. Nothing lost if it doesn't work out and then you can go to re-lining, re-bbling, etc.
Just my thoughts,
