Many thanks for all the suggestions, everyone.
I ended up booking Hiiragiya, based upon the fact that reserving via email was possible, and also because I got a sense (maybe mistaken), from various reviews and recommendations, that although both it and Tawaraya were great, there was slightly more enthusiasm for Hiiragiya from people who had stayed there. Anyhow, I only booked it for a single night, to try and get a bit of the Ryokan experience, and booked the Hyatt for the second night in Kyoto. It was my intention to use the second night to try out another kaiseki dinner, but it turns out I have a good credit to use at the Hyatt restaurants on dinner, so I may end up having the dinner at the hotel....That's one way of saving about $300 on a meal!

...although a tough call....
In Tokyo, I am leaning towards trying Kondo for tempura, but I just can't get my head around how a dinner there could be justified at about $250 per person, for mainly fried vegetables and a few pieces of seafood, even if done 'extraordinarily well'. I am also encountering the same issue for booking high end sushi like at Mizutani; how can it be justified when one can get supposedly great sushi at Tsukiji market for hundreds of dollars less....Which leaves me to Ryugin...$300 for a kaiseki in Tokyo when I am going to try that at hiiragiya in Kyoto?
Confounded! I am very willing, and do in fact, spend big money on major dinners, if I feel the value is there, such as an expensive steak or expensive lobster/seafood....But for relatively cheap ingredients and simple foods, even when done by an artist, I personally struggle to justify it. That being said, PLEASE convince me to go and try these places,; I desperately want to try them....