You can always work push ups and pull ups independently of your workouts. Pavel has the GTG (grease the groove) method.
From what I can understand from your post, you're basically going to be doing the same workout; however, you'll be interchanging squats with deadlifts and chins with pull ups. I don't see a problem with that at all. Now if you choose to do the GTG method for pull ups and push ups, then that would knock the problem of combining chins and deadlifts and what not in teh same workout.
I do think interchanging deadlifts with squats is still a good idea. Even perhaps
F-unilateral leg movement