Lapping compounds will do the most thorough job, progressing through the grades to 1200, followed by Flitz to polish. The problem is you have to disassemble to bolt to ensure you get no grit whatsoever inside and can clean it inside and out to remove grit afterward. You also need to know how not to overlap and loosen things or cut completely through any heat treating that may have been done on the lug surfaces (I don’t know this about Remington, but some Mauser and Springfield bolts have hardened surfaces). Disassembly really requires a special tool to keep under control. Flitz isn't abrasive enough to cause damage, so that can be applied without disassembly. Iosso Gunbrite and MAAS are both polishes that will work as well as the Flitz for this purpose.
You could have the bolt engine-turned. The swirl pattern this produces holds oil and helps lubricate and achieve slick bolt operation. This requires a special indexing jig and a drill press to do well. It also requires bolt disassembly for rigorous cleaning afterward.
If you choose either method that requires disassembly, I would lap the lugs to a perfect fit while you are at it. This can be done without removing the barrel by using a brass rod dropped down the tube to apply the lapping pressure to the bolt face. The bolt has to be centered in the receiver by shims so you don't lap it into a cocked position.
Maybe the Flitz is easiest to try first?
As to the grease, I recommend you go to Sprinco and buy their Plate+ products (
http://www.sprinco.com). You clean the bolt thoroughly with the green bottle Plate+ cleaner and prep, then soak it 72 hours in the Plate+ silver (black really). I believe this material is licensed from a NASA patent. It is a colloidal suspension of sub-micron size pH neutralized molybdenum disulphide. It gets into and has an affinity for metal surface imperfections and crystal lattice interstices (so-called pores). It is sold as a semi-permanent barrel lube to increase velocity a little and to reduce fouling (friction's impact on muzzle velocity is minor - 50 fps or so - which is, therefore, all any lube can gain you). But I like it for reloading dies and moving parts even more.
MolyFusion also works, but discolors the surface slightly, so you may not want it on a visible part like the bolt body. I have yet to try to the newer boric acid based lubes in this application, so I can't comment on them. However, I have had very good luck with Mil-comm's TW-25B. This is the "grease" the military approved for gattling gun mechanisms. It comes in a syringe and you warm the metal and burnish it in. Sinclair International sells it, among others. Mil-comm has a web site, but I forget whether they sell direct?
Nick