V2 is an interesting word order type, and as a speaker of a language with it (Swedish), I am interested at what happens sometimes when the brain exaggerates it by accident.
Swedish permits using intransitive verbs in a copula-like fashion more than English does. English permits similar things - e.g. 'stand tall' - but such examples are far fewer in English than in Swedish. Examples would include "he sits tired", "I went confused to my destination", etc. So basically, conflating both expressing something about physical position or movement as well as something about the state of the subject.
I've noticed that I tend to overuse that construction to reduce the size of the NP to the left of the verb, and I think this is a result of V2 on overdrive.
However, the most extreme thing I've accidentally done is split coordinated NPs on the left and shifted the first half to a sentence-final position:
John brought wine Lisa and
Lisa and John brough wine.
I imagine one could take any syntactical feature of a language and exaggerate it in similar ways, have other syntactical features' use change to accomodate the exaggeration of such a trait, etc. I'd recommend looking at features of your native language (or any other language you know), and exaggerating that trait and having other traits pick up that slack. It'll definitely contribute to coming up with interesting conlanging ideas.