I use small rifle primers in hot .38 Super, 9x23 Winchester and .400 Cor-Bon loads (in cases with small primer pockets). I worked up the loads with the small rifle primers, just like working up any other load.
Small pistol and small rifle primers are the same size, dimensionally, but differ in cup thickness and the amount of priming compound. Large pistol and large rifle primers are different sizes. The diameter is the same, but the length is different, with the large rifle primer pockets being deeper.
In your case, I would take The Bushmaster's advice and just try another brand of primer. As Walkalong noted, you'll also probably have light hammer strikes with small rifle primers, along with the need to work up your loads from the beginning.
If you use Federal primers because of reliable ignition, then my second choice would be Remington, then Winchester, and lastly, CCI, since sensitivity falls in that order.
Hope this helps.
Fred