A key to understand the VMS

[ThomasCoon]

For instance, it seems clear that okaiin is related to otaiin, okol to otol, etc.

I agree on this point. The gallows do seem to form some sort of distinct "letter-class" with similar functions.

Like I said above I think it's also important to consider the fact that q is almost non-existent in the labels.  This also seems straightforwardly grammatical: q is something used in writing complete sentences but that is not needed in labeling individual items.

Sam G is right that q is rare in labels; that's important. For some reason, the process of encrypting a line necessitates the use of "q-" but the process to encrypt a label does not. The answer could be grammatical, but it's good to keep in mind that there are other explanations: perhaps it's part of the Line-As-A-Functional-Unit system or some other line-encrypting mechanism which doesn't apply to a single vord of text.