Strip the bolt as per the above, clean all the bits, check for signs of rust on the bolt inner parts & remove it if present, use a non-gumming oil & apply very sparingly to all parts, (blow off any excess with dry compressed air if possible) re-assemble as per You tube, grease the bolt lug bearing surfaces & rear cam bearers, clean the action bolt lug recesses & the job's done.
I did the T3 bolt last night, which was easy when you know how. So I will clean the inside of the bolt every once in a while from now on, along with the usual brush when cleaning the rifle after use.
I then found a bunch of Videos on YouTube about the Remmy 700 bolt removal, with the paracord loop or heavy plastic coated garden wire in a vice being the 2 most common ways of doing it. I have not done mine yet but it did not look too hard.
Interesting about storing the bolt in the uncocked state: in the rifle vs uncocked out of the rifle before storing in the ammo safe.
Keeping the bolts away from the rifles makes for more security - slows down aquisition for misuse.
Graphite is mucky stuff to play with plus a good light non-gumming oil has corrosion inhibitors in it. A very fine film won't hold much crud.
Also if you keep the rifle cleaned regularly crud build up is not a real issue.