Although terribly undefined is a parenthetical clause (more specifically a free modifier), no doubt, grammatically acceptable. Delimitation by commas does help, though the phrase could stand without them, too.
In essence, a parenthetical is just a phrase that is not essential to the rest of the sentence. However, just because it isn’t essential does not mean that it isn’t important. When used correctly, a parenthetical can add crucial new information to a sentence without disrupting the flow. (University of Nevada, Reno)
But it is true that which although can sound a bit of a mouthful. In such cases, using the more seamless though can help:
our process which, though terribly undefined, had sufficient similarities to...
Both although and though can be used to introduce reduced clauses. (Cambridge)