I'd have every Senate and House vacancy appointed, with special elections held at the general election in the case of Senate vacancies in seats not up that term (don't see a ton of point in 2 month terms). Perhaps there'd be some restrictions, like Wyoming's same-party pick.
You have described the method of replacing vacancies in the IL General Assembly. Here's what the State Constitution says in article 4, section 2:
Statute provides for the method by which parties fill the vacancies. In general it is by the weighted vote of the chairs of county party organizations (or ward and township committeemen for Cook). The weighted vote is based on the votes cast in the most recent party primary.