LGA to JFK transfer plan, need confirmation

We are landing in Chicago the first day at 6AM and want to explore the city for the day. Our flight home (Europe) from JFK in NYC is the following day at 4:15PM. For budget reasons we are considering 2 Southwest flights form Chicago to LGA:

  1. MDW–LGA (20:20 – 23:25) - that means we have a whole day to transfer from LGA to JFK but we need to leave Chicago for the airport at like 5PM the same day
  2. Second day MDW–LGA (07:20 – 10:25) - that means we have more time to explore Chicago and we have time from 10:25AM -> to 2PM (flight departs at 4:15PM) to get from LGA to JFK, is that a reasonable time frame if using public transportation?

The most recommended route here is Q70 to Roosevelt -> E train towards Jamaica -> Airtrain to JFK, google maps says it takes approx 1:25h.