I thicken with whizzed up veg too.
Other alternatives would be whizzed up psyllium husks or whizzed up chia seeds. Never actually done this in a meat gravy, so I wouldn't suggest trying it for the first time on something you are serving to guests!
The problem with all these 'alternative' thickeners, is that they never produce the same texture as traditional gravy thickened with flour - but then for a meal like this, that won't be the texture for which you are aiming.
I wouldn't worrit about the carbs, either.
So long as the steam can escape, most of the alcohol will boil off.
So long as the wine is dry, there won't be many carbs in there in the first place.
You (probably) won't be drinking the gravy by the bucket.
The rest of the meal (fat, protein and fibre) will slow down absorption.
think of it as a trial run. If you see any spikes, then you can do a re-think next time you cook it.
Making me hungry just to write this.