....if, once Willoughby discovered whose ward Eliza was, he was also equally appalled at the idea of having Colonel Brandon as a 'father-in-law'? I'm just kidding about that, actually.

I agree that the reasons he thought it would be 'impossible' to marry Eliza is primarily because she didn't have any cash to give him. As he told Elinor "though the death of my old cousin, Mrs. Smith, was to set me free, yet that event being uncertain, and possibly far distant..." Just marrying Eliza didn't mean that he was definitely going to inherit from Mrs. Smith. Willoughby admits that "She was previously disposed to doubt the morality of [his] conduct in general." There was no way of knowing that he might not do something else to offend her and get written off again. Something like having extra-marital affairs, which I would think inevitable for someone like him, particularly marrying someone he doesn't even care about. Or perhaps another unwed mother of another out-of-wedlock child? It hardly seems possible that Eliza was the first or the only woman he treated that way. There may well have been others before and after her.

And the prospect of Mrs. Smith's death is also possibly 'far distant'--even if Willoughby remains in Mrs. Smith's good graces, it might still be years before he could get his hands on her money, and he needed money ASAP.