Haydon
By the part number you gave you have the early fuel valve. You can confirm this by just looking at it. The main body of the valve is cast. The later valve main body is machined out of a block of aluminum.
I've never had one of the old stye valves apart but they can be disassembled and there is 1 packing part #0413020-4 at the top the seals the shaft that you turn.
As I said I've never seen one so I'm guessing the valve probably works by having some sort of barrel that you turn by the shaft. This barrel is probably a close tolerance fit inside the valve body. I would disassemble it and clean the parts. Probably some junk build up in there which is causing it to bind up.
I just did a search at
http://www.cessnaparts.com and here is what I came up with.
Your valve part number 041320-3 has been superseded by part # 9851085-1 and now cost $516.35. The packing for your valve 041320-4 has been superseded by 38481. They didn't list a price or availability.
If you decide you want to replace it altogether the best bet would be to get the later valve 0513120-5 This currently lists for $899.30 If you go that route you may also have to replace the shaft assembly that turns the valve. There are 2 of these listed depending on the serial number of your aircraft 0511157-8 or 0511157-14. Of course your serial number wouldn't fall under either of those so it would be a guess. Now as far as legality goes replacing the old style with the new I don't know. Talk to your IA.
The easiest and cheapest by far unless your valve is damaged in some way would be to remove, clean and reassemble your current valve.
And one more thing there is a special lube called fuel lube which is not effected by fuel. This is what you would want to use to lube the valve. It is very expensive to buy the whole can given you'll only need a small dab. Hopefully a friendly mechanic will have some you could "borrow".
Perhaps someone who actually has worked on one of these valves will post more.