Another problem with chamber adapters is that they effectively turn a bolt action repeater into a bolt action single shot.
If I were going to try it I would most likely use Trail Boss. Hodgdon's website has data for .308 Win and .30-06 using Trail Boss and Nosler 150gr BT. For both cartridges the minimum charge shows about 1100fps and the max charge is over 1400fps. 7.62x54R data is generally right between .308 and .30-06 data. Going off of that theory the minimum charge for the x54R with 150gr bullet and Trail Boss, the minimum charge would be about 11.5gr and the max would be about 16.5gr. However, I would most likely start with the 10.0gr min charge from the .308 data. I'd be very cautious in making sure both the bullet core and jacket exist the barrel. Having never used Trail Boss personally I could be wrong but I think using Dacron filler between the powder and bullet would be a good idea. And I wouldn't attempt it without a chronograph.
Another option would be to step up to 180gr bullets and use Hodgdon's method of filling the case to the base of the bullet (DO NOT COMPRESS TRAIL BOSS). It wouldn't likely be sub sonic but you can work your way backwards from there, and use Dacron filler, until you reach sub sonic velocity without sticking a bullet/jacket in the bore.
You'll have to make your own decisions, I'm simply telling you what I would do if I desired a subsonic x54R load. I don't know if a Mosin barrel will even stabilize 150gr+ bullets at sub sonic velocities. Calling Hodgdon may be a good idea. They won't give you any definite information if they haven't tried producing such loads, but they might be able to tell you if its a solid theory.