|You sound like a chap after my own heart 'n mind; one of the "olde" school; a cursed and stubborn spirit; one wot won't give up - easily...|
Besides it being possibly an issue wth the sensor, it "might" be the head is just not able slide/track along the arm. (Think of the olde turntables with their tone arm (as was often called) at the end of which was the pickup cartridge assembly. In time the complex of moving parts under the deck could/would slowly glue up/solidify - due to dust and intended lubricant baking more or less solid in the heat in that area.
As in one of my earlier responses here, cd/dvd units have similar issue at times. The arm however doesn't move (the olde turntable tone arm did of course) but the lens/head assembly does.... unless the minimal lubrication there in effect dries out. That can be addressed and the arm/head assembly cleaned and lubricated again; so that the lens/head assembly will slide along the fixed polished chrome/steel or whatever round arm/bar.
Interesting project to play with; suitably reinforced with tea/coffee/hot choccy 'n cookies/biscuits - even cake...
Which having said a replacement unit would go straight in and likely would quite inexpensive? The only issue you might have with a replacement unit is finding one that is the correct connection/interface. Originally they were all EIDE but I think they are mostly SATA nowadays? But likely one can find whichever via eBay, Amazon, New Egg etc.?
Computer fairs sometimes can have EIDE units, as may clearance houses etc.?
A decent slightly longer usb cord would be an investment; I've usually found Amazon good for those. And a wee patch (actually 3 or 4) of velcro on the base would allow you to park the external unit on top of the computer tower, and thus stop it sliding about?
The current slim line units are a pain in that regard, which is why i suggest the velcro option (or even a little double sided tape, or single sided in loops) on the base?