Why don't you just run for 20+ minutes at a nice constant pace? You will lose weight easier that way. You will maintain your strength, trust me. Jesus, I run quite a bit and I would still say Im strong. However, I do run AFTER I lift, sometimes in the morning.
I would not do high intensity interval training after weights unless it was after a small body part like, shoulders, biceps or triceps. better to split it up in the am or pm or save it for non-weight training days
William F. Buckley describes a conservative as, "someone who stands athwart history, yelling Stop." - and then proceeds to drag civilization back to times best left in history's dungheap.