welcome to fun wyfly. I haven't heard of anyone trying what you describe...I think you'd be hard pressed to catch a boat wake paddling a sup foil. Though racers and downwinders can do flat-water sup starts, so it's not impossible ... but it seems like freakish-level fitness and skill to do it.
What I have seen in videos is riders dock starting with a prone foil and then pumping out to ride boat wakes. This is also mega skiilled, but maybe more attainable by an above-average rider, slightly below freak-level (though personally I am working hard at it and still can't yet do the pump monkey thing....I remain at the Peter Garret dancing level).
Finally what is definitely attainable: wing foiling into boat wakes. See the videos of the riders in San Fran bay stealing wakes from ferries and freighters. Your own personal tow-in! Problem is, pleasure boats won't be out on your lake when it's windy enough to wing.
In the end, sounds like you need to sell your car and get an e-foil

PS I have a dream of using one of these e-fins to provide just barely enough extra juice to be able to paddle into unbreaking waves...if I ever receive it (kickstarter) and if it works, I will update my post, as this would be an answer in your situation potentially
boostsurfing.com/