Vinyl Engine has one for the 350. Really, from what I have seen when something has a model nuber like 353 and you find info on one that says 350, it is mostly the same. It may have been just a different cartridge really.
Here is a driect link to that manual :
http://www.vinylengine.com/library/jvc/al-f350.shtml
however you need a membership to get it. If there is soem reason you can't get a memebership I could Dropbox it.
But if you are going to be fixing all this, you should get memberships at hifiengine, vinylengine and probably audiokarma. All free.