Is grift the right word to use here? Is all corruption grift?

All corruption (and other dishonest ways of making profit or advantage) is graft, to attempt sell something under false pretenses is to grift [0].

Grifting is often among the techniques used to effectuate graft.

IMO, the upthread post reads better with “graft” which is a abstract noun, matching the use upthread, where “grift” is usually a verb (I've also seen it used as a concrete now for a particular operation in which the agent is perceived to be grifting.)

[0] Most dictionaries I think will still say this is specific to small-scale swindling, but I think that's a lagging indicator; IME, usage has drifted to be more generalized, with large scale operations often referred to as grifting.

Grift is slang. Graft has a long historical usage, and therefore a well-established definition.