I may have the same gun (Savage 59), and have had the same issues.
To remove my bolt, there is a set screw on the receiver. Remove the screw and then remove the bolt (you may have to pull the trigger to get the bolt past).
I use CLP / Breakfree. In very liberal quantities, soak the bejeezus out of the entire thing and let it sit for a few days to a week.
Use a brass/bronze/stiff nylon brush and scrub away all of the crud that has been lifter by the CLP.
The action should be much smoother by now.
For rebluing, I prefer 'Blue Wonder" as a cold blue. I did the birchwood/casey stuff and it wipes off entirely too easily
'Blue Wonder' is pretty damned strong and seems to hold up well to cleaning----you MUST follow the instructions.
Brownells and Cabela's has it (CAbela's is cheaper)
.
And alot of elbow grease woth 4/0 steel wool and alot of patience in the metal prep will have you a decent looking gun for not much moolah.