You are not exactly correct in describing the situation. This (your) part looks familiar because I have 2 of them on my shelf, unused. This "part" called a lift rod) is actually 2 parts and one(clevis) is slightly bent and the other (lift rod) is about to break if you straighten it. This 2 part link is usually part of a mid-mount mower lift system using cams on the rear 3pt lift arms to pull these links to raise the mower on a lot of JD tractors. I'll bet you can find one from another mower in the on-line JD part system that is identical and has a separate part number (just the broken part of the 2 piece link), I'd guess its a $20 to $25 part all gold plated as such if that's what Mom insists on. As such you ought to do the following:
Unscrew the 2 piece link. Break off the twisted link, put it on you sidewalk and hammer it flat. Get the broken part welded by someone. This could be by yourself at a welding 101 class Adult Ed at the high school. Or have some kid weld it at the school shop. The part is small enough so that you could mail it to one of us and we could weld it for you no-charge (you pay Fed-Ex).
Meanwhile, use a short length of dog chain to substitute for this link until its fixed. All you need to do is measure the length of the other lift rod/clevis link. The price you quote is for the entire link, cam, pins, bolts, yadda, yadda that the tractor would need if you were adding the mower as a kit.
As I said this is the same double adjust link I have on my 15 year old 72" mid mount mower.
Don't make this a debilitating issue. If this is all that ever happens to this tractor it will be a miracle, indeed.
An a/c used buzzbox welder can fix this in 14 seconds (7.0 per side). Practice for 10 minutes and then buzz it.
Or, take it to a muffler shop, pay the guy 5 bucks to do it for you and walk away. Send it my way and I'll be happy to do it for you (U pay 2 way shipping). Meanwhile I will try to find the part number for the lift rod on my mower. It will help if you post the total length of the good link. Dimension is end to end in my assembly diagrahm.