I'm not sure if you can even buy these anymore, but the FBI had the 62gr XM556SBCT3 ammunition designed specifically for 10.5 - 11.5" barrels (SBC stands for Short Barrel Carbine) using the bonded TBBC (T3) bullet. Hornady also produced the 5.56 NATO 75gr TAP SBR ammunition (81295) specifically designed for law enforcement short barrels. Both are soft points (exposed lead), but I find that TAP SBR provides much better precision from my SBR. I believe that the XM556SBCT3 is the gold standard in barrier blind short barrel rifle ammunition.
It turns out that there are many commercially available ammunition that are effective at lower muzzle velocities so long as the target is not too far down range. For example, the Black Hills 77gr TMK round is effective at lower velocities. Federal Fusion MSR and Speer Gold Dot ammunition appear to be also effective at lower muzzle velocities at short range (under 100 meters). Some may provide effectiveness out further, but if you are running with an SBR, I would assume you are thinking a shorter radius. The Black Hills 50gr TSX is also regarded as an excellent round from a short barrel, but the range is very limited because it requires a higher velocity to expand versus other TSX loadings.
All the above are pretty dang expensive, especially now. Some are regarded as unobtanium these days. The Gold Dot and Fusion ammunition were fairly reasonable in price before the pandemic compared to the others. If you find any of the above, those would all be decent choices. There are others I'm sure and others will chime in with their favorites.
ETA: The Gold Dot loading is at .223 pressures and have pretty low muzzle velocities even compared to other .223 rounds. The 62gr that you have will have a pretty short range to be effective.