I ran into the same primer problem back in the 80's (Jimmy Carter's antics were the source of that panic)...no standard primers were available, but I had a considerable supply of Magnums.
In my .357, and .38 Special guns, there was no discernible difference using Unique, 4756, or 7625, the only ones I tried. My loads were just under 1000 fps and I was using a chronograph. Pressures appeared to be the same, but groups were somewhat larger...on the order of 25%. Guns that would turn in 1-1/2" gps at 25 yds, opened up to a little over 2". Not a lot, and good enough for practice.
In 9 mm and .45 ACP, it was the same but only the .45 showed any group increase. Pressures, again, were normal.
In .41 Magnum and .44 Magnum, again with 1000 fps loads, I saw no difference in group size.
All in all it was a non-issue, but again; I was not pushing the envelope at all...just getting some moderate loads for practice and plinking.
Were I, you, I'd use them starting with the entry, starting loads, and work up to what you want, looking for pressure signs on the primers, or if you have access to a chronograph, large extreme spreads in velocity over a 10 round sampling.
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USAF FAC, 5th Spl Forces, An Loc, lll Corps, RVN, 69-70, Vietnam Vet '69-'73