Ways to make a coverb the argument of a light verb in MRS

I am working on the relationship between the light verb and the coverb in a light verb construction where the coverb is the ARG2 of the light verb. This is specifically in the case where the coverb in the LVC is a verb. The example I have been working with (where “go.up.to” is the coverb and “catch” is the light verb) is

Garrin-ngan daab      i-n-nya-gal
hill-ALL    go.up.to  3-TR-catch-REC.PST

He went up the hill. (from Claire Bowern’s A Grammar of Bardi 2012 p. 227)

Emily and I discussed three different ways this could be done:

  1. as a scopal argument with qeq
  2. as a scopal argument without qeq
  3. where the event variable functions as the argument

I was wondering if anybody had any feedback on the consequences of any of these. Thanks in advance!

One thing that occurred to us is that the scopal argument options both suggest that the coverb could be negated separately from the light verb, which we suspect isn’t possible. In addition, the qeq option suggests that quantifiers could scope in between, also really unlikely.

What other differences do people see?