I would suggest trying some different handloads. Every gun has it's favorite load it will shoot the best. Its not alway going to be a floating problem or a trigger. Between the two I would opt for a lighter trigger before going and floating a barrel. Especially a single shot rifle.

You wanted a specific load when you had the rifle in mind. You may have to change that. One thing you can try is buying a box of ammo in the 139gr. and see how the rifle likes those compared to the handloads you are producing. Second thing I would do if none of the 139gr loads work is try a different weight of bullet. And just maybe if none of it works you bought a rifle made on friday afternoon about beer time.