I've heard your playing, so i'm pretty confident in suggesting some p/u's you might like.
I have a custom shop vintage '50's bridge that I like a lot. I paid $42 for it with a vintage Reissue steel bridge included!!! If you're interested in that message me and see if my guy is still pulling those kinds of deals and set up a safe Ebay transaction for ya.
The fender fat 50 and '69 are also very similar in price and tone. The duncan SSL and Antiquity's are as good as actual vintage gems at a reasonable price.
The Fender Twisted Tele neck pick up is the best sounding and usable neck pickup ever, period. I bought one to take it apart and here's the big secret... dum dum dum... jazz bass magnets. But i don't use neck pickups in any of my teles.
Of coarse it could be the grease bucket circuit that you don't like. The hot alnico 3 pickups aren't for everyone but I think that circuit might have more influence on the un-tele sound you are hearing. Maybe, maybe not, but it would be cheaper to try than a new pickup.
But, I urge you, if you are going to try a new pickup to try the GFS custom whatever they call them, they sound awfully good for the price and if you don;t like them you can get just about all your money back selling them.