Recondition my 1986 Thiel CS1.0 or buy new?

Take the store up on the in-home demo. That is the only way you will know for sure. I had to sign up for an in home demo at 1 local store and the salesman suggested picking it up on a Saturday. The store is closed Sun and Mon. Another option would be to bring your speakers to the store but the chances they have the same electronics and room configuration is pretty nil which again you should take them up on the offer.
Good Luck

Elevick, while perhaps not as sensitive as some of Thiels newer models, I think the the impedance load of the Thiel CS 1 is lot easier on amplifiers than the newer Thiels.
Raya, if they're not broken, I'd leave them alone. Though perhaps undervalued on the used market, they're probably not worth $400 on the used market, so the repairs/ shipping appears to be a poor value. They're still good speakers, and I'd caution one against assuming some newer speakers sounding different as actually being better. As much as you might trust your dealer, at this price point, and considering the value of the dollar today as compared to your 20+ year old then costing $1000 Thiels, I don't think the technology has improved that much. I'd imagine you'd be getting a lot less for your 2011 $400 with a new speaker.

I am going to take the store up on the in-home demo. If the sound is only slightly better, I'll stay where I'm at, If it blows me away, then I have a decision to make.

That seems like the best course of action. Let us know how it goes.

I have been trying a variety of in-home demo's compliments of my local audio stores. Last night I brought home the new Monitor Audio RX6. I am glad I did, was getting ready to keep the Thiels and go with a Sub. Simply put, they weren't just a little better then the Thiels. They were a lot better. Highs were more refined and laid back, with more resolution and micro detail. They had none of the grittyness and fatigue I get from the Thiels. Midrange on the RX6 was more open and detailed, which was a surprise. I heard fretboards and fingers across strings and hands on bongo's I had never heard before on recordings I had listened to 100's of times on my Thiels. Bass was definitely more extended, tighter and more controled. I estimate the RX6 go down to 40HZ (literature says 38hz, probably at -5db) Thiels rolloff was 50hz according to old literature. Bass was substantial enough to omit the need for any subwoofer. They were also more effecient, easy to drive, and very forgiving when pushed.

FYI I have also listened to the following Totems (ARRO, Dreamcatcher, & Rainmaker, great detail and imaging, very lacking in what I call the slam factor, need a sub) B&W 684 (I don't get it, very neutral but boring, gave me no excitement, almost thin) Paradigm monitor 7( I have other paradigms for our surround sound in our family room, great for movies but present there own set of problems with music, especially the upper midrange)