RE: Running shots...
We hunt deer with dogs, and I use a .243, a A5 20 ga and a A5 12 ga. I suggest to stay with the shotgun. I prefer the slugs in the 20. If you use bs you will have to use #2 or #3 bs. I have never seen the 20 loaded with anything else.
In the 12 I always used #1 or #4 bs. Just more pellents than 00. Just my thoughts.
Good Luck. Capt Brad.