RE: ejection problem/rem 740
Is the spent casing holding so very tight in the chamber that the ejector can't pull it out? Evidence of that would be that even using a rod pushing from the barrel end out you have trouble dislodging it.
If that's the case, you may need to do some serious degreasing and removal of residue in the chamber with bore cleaner and chamber (copper) brush repeatedly. Same with the barrel, as there is likely significant copper/brass build up. Then only a very light coating of quality gun oil. Stay away from oil/lubricants that have additives like teflon that over time and in cold weather make the action very stiff and hard to eject.
If the brass does come out with a cleaning rod easily, then you may have a problem with dirt ejector leaver and/or ejector spring. I don't know how easy it is with the 740 to get the bolt out. If you can, maybe soak it in bore cleaner, brush it with a gun cleaning brush, then spray it thoroughly with bore cleaner before putting a light coating of lub on the moving parts and wipe of the excess.
Check to see that the inside of the ejector that engages the cartridge. If it's worn, you can get replacement parts.
Good luck!