The LX seat uses seatposts with the Miyata bolt pattern. The KH seatpost you linked uses the Schwinn bolt pattern. The two are incompatible. I don’t know of any 27.2 Miyata seatposts, and so if you want to do it you will have to use a shim to get your seatpost to fit the KH frame, or see if you can somehow re-drill your LX seat to fit the Schwinn pattern.
As for crank extractors,for occasional use they are all pretty much the same. Unless you are using it a lot you won’t appreciate the little details that make the better ones better.