If you have a way to secure your rifle in an upright position muzzle end down with a catch vessel under it [or have someone hold it for you] I'd get one of these wash bottles fill it about half full with charcoal starter or other [petroleum distillates] solvent [one could also use Ronsonol which is mostly hexanes] and just wash the the thing out until the wash solvent comes out clean. Wipe out the recesses with something like an oversized [3 inches] dry patch and push a wet patch followed by a dry patch down the bore.
Nonpolar hydrocarbon solvents are great for removing most oils and greases. For me the main thing to be cleaned out is bolt lug lube.