Some cats are rather bouncy and they don't seem to ever stop being bouncy. However, that is not the majority of kitties.
You can change a dose during a bounce. What you want to try to avoid is changing the dose during the cycle when a bounce is breaking. The downward momentum of the bounce breaking coupled with a dose increase can make for a bit of a wild ride. However, if the bounce isn't breaking, it's less of an issue. Keep in mind, that the expectation is that when the bounce clears, your cat should return to around the numbers he was at pre-bounce. So you do have some clue where the nadir should be and when to increase the dose.
You are testing enough to consider TR. FWIW, I used TR and worked full time. I don't think it's an issue to use SLGS with a cat that has experienced DKA. At the moment, Tigger's ketones look good. It's more of an issue to be aggressive with insulin if ketones are present. Frankly, I don't care which dosing method you're using if ketones show up. All bets are off and the single goal is to get the ketones under control. You must maximize the insulin, get water into your cat, and keep your kitty eating. (I've been known to tell people that I don't care if they are feeding their cat hot fudge sundaes -- minus the fudge sauce -- if that's what it takes to get their cat to eat.) It's entirely your call. If it were me, given how high Tigger's numbers tend to run, I'd consider TR as it will be more aggressive about getting him into a better range more quickly.