Editing Counting objects

Some languages simply combine numeral + object:
: three beer

The problem with this is that it makes it impossible to use numbers in compounds, e.g.:
: three month

Does this mean ''three months'' or ''March''?

On balance, I think being able to use numbers in compounds is more important than being able to use numbers without connectors.

So we need to say something like:
: three GEN beer
: beer ADJ three

(I'm really not sure what the head and dependent are meant to be here. It requires some thought.)

Then there's the case of using counters, like ''three bottles of beer''. I guess the following could work:
: three bottle GEN beer

Grammatically speaking, it means that ''three bottle'' is a compound. This isn't a problem if the counters are well-defined, but how would you say ''a three-month holiday''?
: three month GEN holiday
: holiday ADJ three month
: holiday ADJ three GEN month
It's getting confusing, to be honest. The first one could mean "March of holiday" (which is nonsensical, but not necessarily to beginning learners), the second one could definitely mean "the March holiday", and the last one could potentially be read as "the month's third holiday".

We need a structure that always works, so perhaps we need a new particle so that we can say:
: three CNT beer
: three bottle CNT beer (''or'' three CNT bottle CNT beer?)
: holiday ADJ three CNT month

It's still a bit confusing.