I've played around with subsonics, both jacketed and cast, for .303 British, .308 and .375 magnum. I've never had a stuck bullet, but I was scared I was going to get one before I started actually shooting them. I prepared ahead of time by getting a bit of steel rod that would fit down the bore... then I wrapped electricians' tape around it so that it wouldn't damage the inside of the barrel if I had to use it. There is quite a bit of tape on my rod which locates the centre of the rod well in the middle of the bore.
Tapping a stuck lead bullet out of a bore shouldn't be too difficult. I've tapped a lead slug through a bore so I could measure the diameter, and it was easy to do. I guess you just have to make sure that the bullet actually exits the barrel after every shot while you are experimenting.
I used only Trail Boss for the .308 and the .303. Like everything I've shot through the old Chrony I noticed some variations in velocity, but perhaps this might have been partially due to the changing light conditions with the Chrony just recording what it thought it saw. Dunno. Anyway, despite the velocity variations, my finished loads grouped plenty well enough for hunting purposes at practical subsonic hunting ranges.
In the .303, 9 grains of Trail Boss gave me about 950 fps with a 150 grain jacketed bullet. Lead bullets don't seem to need as much powder for the same speed. 7.5 grains of Trail Boss behind a 170 grain cast .308 bullet gave me 1050 fps. And although the larger bore of the .357 isn't a good comparison, 4.2 grains of Trail Boss propel a 158 grain cast bullet out of my .357 barrel at around 945 fps.
I haven't done extensive testing, but at one stage I thought that "Fryxell Lube" on my bullets gave me a few more fps compared to a a more basic lube that I'd been using at the time. Fryxell Lube is a mix of molygraph grease and beeswax. It smells a bit and can be messy.
Does your bullet design and your rifle enable you to perhaps not seat the bullet quite so deep so you can fit a bit more powder in? Just a thought.
I too would be thinking about using AP70N powder. Or maybe even APS350. But 'proper' data for such loads may be hard to find.
A 150 grain cast bullet travelling at 800 fps is still going to penetrate. And they should be relatively quiet. I will be interested to hear how your loads perform. Best wishes from Nelson.
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