I was in a similar predicament. I wanted to do some Grouse and Mt. Quail hunting during deer season, but I did not want to miss an opportunity on filling a second deer tag.
California F&G Code.
§311. Methods Authorized for Taking Resident Small Game.
b) Shotgun shells may not be used or possessed that contain shot size larger than No. BB, except that shot size larger than No. 2 may not be used or possessed when taking wild turkey. All shot shall be loose in the shell.
The quoted law only relates to California.
We stopped at the F&G office in one of the least populated offices in California. I told a warden that I would like to carry rifle slugs for deer while out hunting grouse and quail.
He felt a little insulted that I asked the question. His basic response was that they were not stupid and would understand why I was carrying the different loads. With his Lieutenant looking over his shoulder he told me it was no problem.
I was talking to a veteran warden. Frankly, if I were in Southern California I would ask the question again.
The hunting regulations for most States can be found on the net. I suggest you read them, and then call or visit the warden and get an eye-ball-to-eye-ball answer.