OK, now we are beginning to get someplace.
1. You have never fired .38 Special in that gun. Gun is "squesky clean" We'll assume this includes bras brushing the cylinder chambers at least once. (Proposed Problem Eliminated)
2. Loads fire fine using magnum primers and you are using a published load that states magnum primers can be used.
...Discusson: There are subtle differences in the measurements of primers from batch to batch, lot to lot, mfg. to mfg. The magnum primers might well be a tad longer than the standards. I've experienced trouble loading small rifle primers deeply enough in 32-20 cases, where small pistol primers do just fine. The height of the primers appeared the same on a dial caliper, but a digital micrometer shows the rifle primers to be a squeak longer. Three of my manuals show only magnum primers with every .357 H110 load and the others make no recommendation for primers.
...Conclusion of magnum primers discussion: Magnum primers are fine, so long as you approach maximum loads data VERY CAREFULLY and watch for pressure signs.
... Note: Because the misfires do not fire the primers, we are not seeing the increased flame front of the magnum primers being a factor in this problem. The problem is that the primers are NOT FIRING when struck, so the extra oooomph of the "magnumitis" is not a factor in this problem.
3. One lot of cases: I would grab a mixed lot of cases and try them with that same load, with a few of the loaded rounds using the suspect remington brass. Any misfires, segregate to inspect the head mark. If they are all the remington cases, you have found your problem. If you get misfires on other brands, also, we are back to square one.
4. Other powders: I use several powders in my .357s. For full power, I use either 2400 or 4227 in the long barreled (over 4") ones. Those two powders are the work horses of my field/defense pistol loading, except 9mm. There are many loads in the books for them and all those I've tried work well. Sometimes I use magnum primers and sometimes I use standard primers. The powders don't seem to need to be reduced but about 1% to 1.5% with magnum primers to get back to the chronograph results of using standard primers.
...Discussion: When converting a load to using a magnum primer, reduce your standard load by 3% to 5% and work back up. The flame front on a magnum primer is hotter and of longer duration than that of the standard primer. This imparts a little more energy to the load and ignites more of the powder on the initial flash, each of which raises your chamber pressure somewhat.
This is probably much more information than you need or want, but hey, that's me.
1.Yes you may use magnum primers with H110 in .357 with the 158 gr. bullet.
2. We don't know what the answer is to the misfires, but STRONGLY suspect it is deep primer pockets or short primers.
3. There are many other powders you may use with the .357. Conlult your manual(s) and follow their guidelines. 2400 and 4227 are old time favorites.