A really soft load will require a softer recoil spring. I have several springs for a Glock and carry it stock mostly with the stock 17lb. spring but use a 15lb. spring when using soft handloads at a range or match. It won't cycle the softer range loads I make otherwise, it'll do exactly what you describe. I load all my own too, except .40, +P and +P+.
Look to Wolff for springs. They usually carry all sorts of springs for all sorts of weapons. I'd be shocked if you can't find 'em there. While there go ahead and pick up springs for all your other shit, they're great quality and the AR packs are nice to have on hand.
So if you can't find reduced power springs for your pistol, what you can do is just buy another stock one and cut one coil off and try that, make your own. Then two if you still have problems and so on. Usually doesn't take much. You can do it with the one you have but I think it's wise to keep a stock one handy regardless.
If it's a spring problem, I'm betting that clipping one coil or reducing it a pound or so will fix it and it'll work suppressed or not with whatever ammo. That's just my guess. Sometimes it's better to clip one end vs. the other (it'll be obvious) and after clipping it, it's usually a good idea to file or grind the cut flat so the spring rests flush against whatever.
What powder are you using? Thought of trying a different one?
What about the bullet? Is it THAT particular bullet maybe? But you say it works unsuppressed...
Typically a heavier bullet will assist in cycling an action but you gotta have enough "umph" behind it and heavier loads use less powder to begin with. You need enough gasses to do the job. While the 115's and 124's are lighter, they require more powder and hence more gasses.
Another factory load to look at is the Hornady XTP. There's another FMJ version with the same profile. Accurate and slow enough to be subsonic, my preferred OTC load if I have to buy factory stuff. It's also a good bullet to load.
Somebody makes a 158gr. 9mm bullet but I don't have any. You could try loading those, and if they cause the same problem then you know it has to do with heavier bullets not cycling the weapon. The fix will be the same though, more power or weaker spring.