How to convert a genus name to a noun or adjective
I think that it boils down to taking a Latin name and removing the case ending to get an acceptable English adjective. Given that it might be a purely linguistic situation, it's possible another SE site would be better (English language?), but this topic is definitely relevant to biologists, as they're probably the ones who run into it most frequently.
We can look at IAPT article 60.10 and it suggests a systematic way to do this, albeit for an unrelated reason. I don't see that they directly address the anglicized Latin adjective form:

A noun or adjective in a non-final position appears as a compounding form generally obtained by
(a) removing the case ending of the genitive singular (Latin ‑ae, ‑i, ‑us, ‑is; transcribed Greek ‑ou, ‑os, ‑es, ‑as, ‑ous and its equivalent ‑eos) and
(b) before a consonant, adding a connecting vowel (‑i- for Latin elements, ‑o- for Greek elements).

I think that we want to apply step (A) but not step (B) here, as their goal is the formation of compound names, and step A alone will get us -id, which is an anglicized adjectival ending (-idus --&gt; -id).
Taking your examples:

Cambaridae --&gt; remove Latin genitive suffix -ae --&gt; cambarid.
Procambarus --&gt; make Latin noun into the adjective procambaridus --&gt; remove suffix -us --&gt; procambarid.

Unfortunately, it looks like there are a ton of possible Latin adjectival endings- the -id examples seem pretty straightforward because you can get an English adjectival ending directly, but other taxonomic names don't resolve so neatly. For example, if I want to use &quot;Lachnospiraceae&quot; as an adjective, I could imagine the following (applying only step A above doesn't seem to work well: &quot;lachnospirace&quot;):

lachnospiraceid
lachnospiraceal
lachnospiraceous

and I don't really know how to pick among them!
I have left a comment on a blog post from Stephen Heard on a related subject (comment above), perhaps he'll see fit to weigh in here.