Hi Joe,
Don't use varnish stripper as it is a stronger version of the normal paintstripper and it will damage your rod.
The best way is to remove the old rings by cutting through the whipping with a sharp knife. When you cut through it do so on the foot of the old ring then that way you won't cut into the blank.
Remove the bulk of the whipping this way and then unravel the rest.
To remove the varnish get some wet and dry paper (180, 400, 800) and some soapy water. Remove the bulk of the varnish off with the 180 and then finish with the finer grades.
It takes a little elbow grease but it'll be worth it in the end [

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When rewhipping new rings on, position them so that they follow the natural curve of the blank and the butt ring around 20inches away from the reel seat. Hold the one of the feet of the ring in place with some sellotape until you get the right location and then build up the whipping on the blank first and up onto the ring's foot.
A handy tool to use is a fly tyer's spool holder as this allows you to get a good, clean whip around the ring.
Once all the rings are in place get some 'Dope' (not the smoking type lol) and give each whipping a coating of this first before applying the varnish. This will help tighten the thread for a secure hold [

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Allow each section to thoroughly dry before wiping down with the 800 grit (wet) to remove any bits and then add a final coat.
It's better to put on two thin coats than one thick one [

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All done then get out and give it a whirl - and don't forget to tell us how it went
Dave