The way the rules are set up now, “on the team” and “in the recruiting class” are the same exact thing.
You’re not being realistic if you think someone is going to go to LU over another PL school when one of those schools is offering $15,000-$20,000 more per year than LU is. Kids are not choosing PL schools because of football. They are choosing to play in the PL because of the education which is basically equal at all PL schools. It boils down to $. It did when it was non-scholarship and still does now with scholarships. Kids go to the school that offers them the most $. Not only for the obvious financial benefit, but the thought is the school that offers the most $ wants me the most. I would think the other factors you mention come into play when the $ is equal.
There is a slightly better chance on beating a CAA school like Maine or UNH that offers 3/4 while LU offers 1/2 because of the education, but beating another PL school is not realistic IMO.