Why not make things a little easier and make it 2x a week lifting? It would allow you to recover from day 1 to day 4 and then still be able to hit conditioning on you work days.
You could then rotate which lifts you hit for 5/3/1, and probably hit sets of 5 in the 70-80% range for the other lift. This way you can recover and make progress without pounding yourself with 4 days in a row.
Press 5x5 @ 70%
Deadlift 5x5 or 5x3 @ 70%
Squat 5x5 @ 70%
Bench 5x5 @70%