Will varying from barbell to dumbell to trap bar to sumo style deadlifts be enough of a variation to allow me to use heavy deadlifts week after week?

Depends on how heavy you go and what your weak points are. It’s common knowledge that you can only max (100+%) on an exercise for 2-3 weeks, but I don’t know about the circamax stuff (80-90%1RM). Try it for a month and see what happens. If it doesn’t work, try alternating heavy deads with heavy good mornings. I notice that I can completely ignore deads if I work on the squat, GM’s, and abs. As these exercises go up, so does my deadlift.

The problem is not whether varying the style of deadlift will allow you to perform them every week, but it is rather- will your recovery ability be able to tolerate it- especially with other leg and back work. You need to be careful not to overtrain. A good indicator that you are not overtraining would be increased strength in the big lifts such as squat, deadlift, and bench press. I would not deadlift on the day before or after a leg workout or back workout(if you perform them on a separate day). As for variation, it is good to mix up things now and then, as the body adapts and needs to be surprised with new movements now and then.

Ed, assuming by “heavy” you don’t mean “to failure,” sure, change-up your deadlifting style week to week. It cannot hurt you. The important factor here is that you are indeed performing deads each week. Good for you. I would not recommend going to failure every deadlift workout, though; as others said, your recovery will certainly lag.