Calling recursively looks clean, I may change mine here to do the same. But you use the flag to avoid endless recursion (in some weird potential "NURBS universe"). I don't like the flag as an exposed interface (#736 (comment))

How does v+(1-v)*0.000001 work if v=1? I think you meant v+(0.5-v)*LENGTH_EPS.

You need to pass a tolerance to Equals, IMHO the default is too big.

Check tv first. So far I could not figure out how to construct anything pinched along a u edge. Makes it faster by avoiding a check that may never be true with the current construction tools.

"sungularities" = singularities

As for my overall opinion on the "numerical" (vs. logical) approach - did you take a look at this?
#736 (comment)

How does v+(1-v)*0.000001 work if v=1? I think you meant v+(0.5-v)*LENGTH_EPS.

Oops. I started out thinking a weighted average so 0.99v + 0.01(1-v) and then was thinking something more like what you suggest. Brain just didn't write either one correctly. I prefer (0.5-v). Isn't LENGTH_EPS really small?

Using the flag to avoid infinite recursion just seems like a good idea, especially if you want to use such a tiny movement. Like I said before, it also allows flexibility at the call site but we don't really need that once it's fixed.

EDIT: hahaha joke is on me. LENGTH_EPS = 0.000001

You mean switch the order? OK. Does that mean you're ok with "check result and retry" vs the "check for degenerate curve and pre-emptively move u,v" ?

This one is shorter, that is it's advantage. The other one is faster (but I need to measure, this is just based on amount of calculations) and "more correct" (whatever that meas) but more verbose...

The problem is that I have not had time to work on it more...