The Kohler engine has a model number that I would use to check what actual Kohler engine is fitted.
Not being a Husqvarna dealer I can not check what engines were fitted to your mower.
There could be several different Kohlers that are rated at 25 Hp.
Some might have a low oil cut out, some don't.
Some might have a SAM ( Smart Advance Module ) most don't.
Some have EFI although we can rule that option out.:laughing:
The key is the model numbers from the engine.
And yes there are a lot of mower forums out there and each one has it's own style.
I am on 9 of them + 4 chain saw sites + 7 motorcycle sites.
However I only post on a few.
Some are a total waste of time with lots of people posting me toos , or offering loads of encouragement & blessings but little in the way of useful help.
There are even some where totally wrong information seems to be the norm.
Some seem to specailize in restoring old mowers .
This site is much like Fix it.
People post a problem and some one walks them through it then they tend to vanish till they come up on their next problem.
I came here to learn about what I did not know ( more that I thought ) and of all the sites , apart from single brand sites, this had the type of responses I was looking for.
You seem like a person who knew their way round a mower and from you original thoughs can sit back & make objective conclusions, which I agree with, there is a fuel problem.
One thing I forgot to mention, put some WD 40 or similar goop in a trigger pack and the next time the engine starts to play up spray it liberally around the manifold ( not easy on a V twin ) annd see what happens.
Clouds of white smoke = air leak around the manifold.
Some Kohlers have a plastic manifold which can warp a bit when hot.
As for the information.
I do not believe in keeping secrets.
Teaching a person how to fix their mower is much better than telling them which nut to turn.
So the more you know & understand the better equiped you will be to diagnose future problems.