Actually those who are strong in the Force and train heavily in lightsaber combat become extremely skilled swordsmen. The ability to use those deadly weapons at such speeds requires the heightened reflexes of a Jedi.
I simply do not see any evidence that war damages a Jedi's combat skills. While Force sensitivity heightens the Jedi's reflexes and awareness of their weapon, the actual strength of that connection is not tied to their abilities with a lightsaber. I think this is rather clear also when Yoda and Dooku are having their little force showdown, and realize that they are at an impasse. They then resort to lightsabers, a wholly different arena.
Also Dooku was being beaten slowly but surely. He was 'delaying the inevitable' against his former master.
It is likely that combat instructors rotated out, but the time that they get to train these students is not very long. Mastering the use of a lightsaber takes time (unless you are a Skywalker, but that's kinda like cheating)
The instructors during these times of war would have most likely had combat experience. As a lot of information regarding particular Jedi is rather sketchy, we can only infer things about how the Jedi were trained, and by whom. Since it is common for soldiers to rotate in and out of combat in order to keep them from burning out, we can only imagine that many Jedi must have done something similar during periods of sustained conflict.
Luke had the knowledge of the entire Jedi Order to guide him in his learning as well as the teaching of others. This includes Cin Dralligs teachings on dueling and the seven forms.
In between these periods of sustained conflict, the Jedi who had fought in the war would have been instructing the newer generations, passing on their practical combat knowledge. Naturally, the First Jedi Purge would have seriously hindered the education of future Jedi. But with someone like the Jedi Exile (an extremely experienced warrior) to begin their training once more, they would have a good starting point. I would also point out that Luke Skywalker was in a very similar position following the Dark Times, and that he was able to train some extremely accomplished duelists.
Correction: Obi-Wan mastered Soresu, Dooku mastered Makashi, and Yoda mastered every form and mastered Ataru to the highest extent. It has been said that Kenobi and Dooku were THE masters of their chosen form.
Another point, Master Kenobi. You've acknowledged him as one of the foremost swordsmen of the Jedi order, and yet he specialized in Soresu (with a dash of Ataru thrown in). Likewise, Dooku favored Makashi almost exclusively and was able to go toe to toe with Yoda (a student of every form, but mainly a practitioner of Ataru).
In the ROTS novelization, Sidious cut down Tiin and Kolar in seconds. His speed caught them unaware. Not that they were going to last long against the most powerful Sith Lord of all time.
This isn't terribly relevant, but Kit Fisto's feat of "surviving briefly against Sidious" is less a product of his skill with a lightsaber and more due to the fact that Sidious just killed the other two Jedi first. He had a chance to raise his guard while Sidious dispatched his companions, but barely managed one or two parries. There are very few good things to say about his decision to "master" Shii-Cho.
Sidious was bringing his skills with the blade to bear on Mace Windu. He wasn't holding back in the duel. He only held back his Force power, and even then they reached a stalemate until Anakin arrived.
And, yes, it's "G-Canon" that Windu defeated Sidious... but it is also perfectly plausible that Sidious WANTED Windu to defeat him. Windu wanted to arrest Sidious, and Sidious wanted to drag out their encounter until Anakin arrived. He needed to make himself look vulnerable and appeal to Anakin's suspicions that the Jedi were planning against Palpatine.
Except for the FACT that Yoda was preparing the Jedi Order for another war with the Sith. They learned from the previous wars, adapting their fighting styles, connecting themselves with The Force. Under his tutelage, the Jedi Order greatly advanced their skills in dueling, their prowess with The Force, and their battle tactics.
So, to conclude what I'm saying here: Jedi do not necessarily thrive on warfare, but it does hone their combat skills. The idea that the PT Jedi order had "mastered the art of lightsaber combat" is quite farcical. They did not have a fraction of the experience with combat (read: actual lightsaber duels) that the Jedi during the times of the Old Republic did. While the Jedi suffered setbacks during the First Jedi Purge, it seems quite clear that they recovered (much as Luke Skywalker's NJO did) and during the Great Galactic War they certainly got back on their game to fight the Sith.
And to say that they don't fight in actual duels is simply false. From the point that they learn to properly hold a lightsaber or training sword, they take part in sparring with other students. This progresses to the Initiates tournaments and finally customary duels between Jedi Masters. You will probably say that a friendly duel is far more different than a life or death situation. It's really not. Especially considering the weapon that they are using. One wrong move, one mistake, and you're dead. This taught Jedi to keep their guard up and stay at the top of their game.
Of course I'm not saying that the Old Republic is completely and utterly out-classed. What I am saying is that you have grievously underestimated the dueling prowess of the great masters of the Jedi Council of the Prequels.
There is not evidence to suggest that the few notable swordsmen to emerge from the Clone Wars era were exponentially more skilled than their Old Republic Era counterparts. In fact it seems that the body of evidence points in the opposite direction.
You asked for it, I guess.
P.S. While I welcome Beni's feedback and counterarguments, I'd love to see anyone else weigh in on this discussion as well.