Here's a crazy idea.
This is still a verb, not an adjective. It just happens to be modifying a noun. It can still take direct objects and do other verb tricks if you ask it nicely enough. (But these can end up sounding a bit odd, just like calling-people rates would.)
There are lots of times that the rate of VERBing gets called the VERB rate. And it doesn't happen with only rate alone. The rate of writing is the write rate. The rate of failing is the fail rate. The rate of passing is just the pass rate.
If people are always taking or giving a penny or two, you could have a take one rate, a take two rate, a give one rate, and a give two rate. That take one is not an adjective: you couldn't have a very take one rate or say that the rate is take one. Just as when you have a rate of giving two, that giving two bit is not a noun but a verb phrase because only verbs have direct objects, so too with a take two rate.
That's why you won't find a take two in the dictionary. It's not a noun, just an ad-hoc verb phrase modifying a noun phrase.
That's also why you shouldn't expect to find an overtake in the dictionary let alone an overtake quickly there for those rates of overtaking quickly if they get called overtake quickly rates.
The chance of working late versus that of quitting early might be the work late chance and quit early chance.
Sure, some of these come off sounding a bit casual or creative, and some verbs are going to resist it. But calling them verbs in modifier roles, not adjectives or nouns, makes it a whole lot easier to explain why you cannot have a very overtake early rate for a rate of overtaking early.
Can a verb phrase take on a modifier role?
Thinking things over a bit, he decided it could.