Has to be said... your blackout will do it better and with LOTS more loading options and way fewer headaches.
Otherwise....
Have had good luck with the 3030 style bullets like the flat nose 150s and the rubber tipped ftx ones too. 180 and 220 round noses do well too and eat up some case volume. Match bullets loaded backwards fly ok and eat up case space.
Trail boss and tin star of course if you're fortunate are the easy ones. Titegroup has data from hodgdon!! and red dot can do well too in my experience. Unique can be workable as well sometimes, though I'd prefer it fill the case better.
You need a fluffy fast powder that is easy to light and insensitive to position in case. Some guys drill out primer holes to make SUBSONIC ONLY brass and or use magnum primers. Sometimes this helps and is worth a shot if you dont get what you need with standards.
I've seen a few reduced volume cases in 30-06 and .308 guys have had made. Nice ones made on a lathe and poor folk ones with epoxy and a drill. THAT first one is a great solution if you can do it or get them. Last I saw they were like 10 bucks each at a gunshow here... not that helpful now unfortunately. Wish I'd have bought some.
If you venture into the world of fillers, a little dacron stuffing lightly put into the case against the powder opens up lots of options. AT YOUR OWN RISK of course. I've used it with success, but generally not needed with a good powder selection. Plenty of information for and against it out there along with details on the light fluffy powders to use with it. Weight of filler counts towards bullet weight and DO NOT pack fluff in there hard; it must stay fluffy between bullet and powder. Again, at your own risk. This is not considered normal loading practice anymore
Also consider a cast bullet. Much less likely to get stuck in bore and easier to remove if you do stick one. Also have had a few instances where cast was MUCH more consistent than jacketed.
Discussion on poverty style custom reduced cases here : )
https://www.snipershide.com/shooting/threads/subsonic-308-loads-with-unique.9642/
If you venture into cast bullets your options will expand quite a bit. These guys are a great resource If you go that direction.
This may be useful as well. These guys have a lot of reduced and oddball powder data for many cartridges.
Reloading Data for cast bullets, result of lever gun accuracy studies on cartridges: 357 Magnum, 41 Rem Mag, 44 S&W, 44 Russian, 44 Magnum, 444 Marlin, 45-70 Goverment, Pistol Powders, Large Capacity Rifle Cases
gmdr.com
All at your risk of course!