'af kappi' looks familiar to me (vigorously, energetically, with a
will), but not 'láta ganga'. I haven't read enough though to know
if that makes it uncommon. Maybe I've seen it and forgotten...
Zoega has a couple of examples of 'láta ganga', ganga 10, but all
transitive. That aside, they do seem to express pretty much this
idea of really letting rip!

láta höggin ganga
rain down blows

létu ganga lúðrana
blew the trumpets vigorously
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Zoega also has 'e-m gengr til e-s' "one has some reason for doing
something"

en þat gekk mér til þess, at ek ann þér eigi
but that was my reason for that, that I didn't love you

Gwyn Jones translates the line in Hrafnels saga:
eigi fyrir því, at þér gangi gott til
yet not out of any good will either

'gott' is the reason not.

On the other hand, Zoega also has a similar idiom with a different
meaning: "to fare [in a certain way, well or badly]".

Hversu hefir ykkr til gengit?
How have you fared?

Loka gekk lítt til.
It fared ill with Loki.

Perhaps it the context that suggests the former meaning. Presumably
she wouldn't know how she was going to fare in advance, so it
couldn't be because of that that she was talking.