I want to thank "WrenchGremlin" from the Virago Tech forum for posting this bit of information in the forum for everyone.

I finally got my bike to run great - it took about a month of taking every little thing apart (some several times) and I have learned a bunch and found great info on this site to guide me. No one issue was key, rather it was a cluster of issues with the TCI unit being the last. The bike would idle fine, surge with almost no power to 3500 RPM then blast off and run great all the way to redline. After the bike warmed up a bit I noticed that I lost spark on the rear plug. Taking the TCI apart and using acetone and a toothbrush to remove the weather proofing from the back of the board, I found a bad solder joint on a green capacitor. This controls the spark timing. Touched up all connections with new solder and tested in the bike - ran like a new machine - very smooth. Attached are the critical points to inspect on your TCI. 10 minutes with a soldering iron can eliminate a lot of problems with this unit.

Other issues corrected:
* carburetor breathers were shot, letting little fragments of dried up foam clog things up.
* Replaced floats, fuel needles dried out or eroded.
* Jetting was incorrect, replaced #128 with #132 per manual spec. (all things are stock on this bike).
* Pulled and cleaned all electrical connections on bike.
* 4 wires going into left side of engine case (wrapped with electrical tape), were soaked and the insulating covers were working their way off. Replaced with shrink tubing and soldered connections.

Went from bike never really warming up and surging, to a bike that takes only seconds to warm and is smooth.

'85 Virago XV 700