…And there I unthinkingly ended that sentence with another verbal noun.

Another way you could say it:

“Tá mé ag goil anonn go bhfaighe mé greim bia.”

Agree completely with above.

May be this example will help you, remember it’s a verbal noun coming at the end not the verb.

Tá mé ag dul anonn chun greim bia a fháil.
I am going over there to get a bite to eat.