Danger from the SSS load is due to inappropriate barrel twist. The 60-grain bullet in a "normal" .22 rifle's barrel (1/12 or 1/14 twist) is likely to not be stabilized properly, If it's not stabilized properly, it's likely to strike a baffle in the suppressor, causing damage.
The Remingtion subsonic 38-grain HP load is the subsonic load I almost always use; almost always out of a CAR-15 with a conversion kit. (I hardly shoot my bolt action CZ or 10-22 anymore.) I've tried the SSS through the CAR, but it won't cycle my gun's action [or the 10-22's], and it's much louder also. Ejection-port issues more than anything; in a bolt-action, this wouldn't be an issue.
I've also tried the CCI "Green Tag", and the CCI "Subsonic HP", but keep coming back to the Remingtion. It's cheap ($1.89 at walmart everyday, and I've picked it up for as low as $11.99 a brick one time), and it's much more accurate from my gun's 1/9 twist than a 38-grain bullet should be. (YMMV on that; .22's are notorious for being finicky about ammo.) I've even tried the RWS "match" stuff, but it's not enough better in my gun to be worth anywhere near its price.
The only thing I'd change about the Remington load is that it's not a copper-plated bullet, just waxed lead. This gunks up the gun and suppressor fairly quickly. But I've yet to find a copper-plated subsonic .22LR; if I ever do, I'll definitely check it out.
The only thing I can recommend is blow a little money trying a handful of different loads. What my gun likes, yours may hate, and vice-versa. Two or three dollars apiece for 6 or 8 different loads to experiment with may make a real difference in how happy you are with the gun.