That's a nice idea, but would also be easy to abuse, for example with death protection (which Tikki hates, but the free dodge after DP might be worth it). Also by fighting low damage enemies to trigger the guaranteed dodge, then using that on the boss. But at least it would require healing before it can be done again. This allows for huge abuse with regen though: regen to just past the HP threshold, hit a low damage enemy to take you below the threshold and trigger the dodge, hit the boss (taking no damage), go regen just past the threshold, attack the low damage enemy to trigger dodge, etc. Also I think it's too complicated.
Maybe all dodging could be changed to work like the quicksilver potion, stacking up when you get hit and resetting when you dodge. Values would need to be adjusted of course, but this would provide some degree of reliability and allow interesting tactics without too much potential for abuse (desecrating TT's altar or using a really big sword to give low level enemies first strike and using that to stack dodge is the only abuse I can currently think of). Also there would still be some randomness in the mix, because if you don't use the stacked dodge you might lose it when you don't actually need it, and the more reliable it gets the more likely you are to lose it while stacking it up further.