I know more about DL interpretation than WDW, but my understanding is that if you call at least 14 days in advance (I would call at least a month - call now if you know which tour you wish to take), an interpreter would be provided for the tour.
Tour guests are given head-sets and the Tour Guide speaks into a microphone, which feeds into the ear phones. This may help a little bit with filtering out background noise and amplifying the sound you are able to hear.
When you call, make it clear that you are Deaf, and that ASL is your first language. I have discovered that if people (any company, not just Disney) believes you can "get by" without accommodation (like my saying I can walk a few steps suddenly means I can leave my wheelchair and walk for a half hour or up a flight of steps), then they may be less helpful.
I am pretty certain that if you call (to other ASL users - would Special Services have a VRS capability or TTY number - I am not certain the Call Centers would know where to send the call), and give them the date and time of the tour you wish to take, tell them you are Deaf, ASL is your primary language, and require an ASL interpreter to be present, they will make it happen.
On the day of the tour, let the Tour Guide know that you also read lips, and that whenever possible you would need to be close to him/her and have him/her facing you.
Also, what attractions, if any, are part of Backstage Magic? The handheld captioning device may be helpful for attractions - my thought was about lower light conditions.
It has been my experience that Disney is more than helpful when it comes to accommodating disability, including providing interpreters (the trick is knowing they exist). If the first person you talk to does not have answers, ask to be transferred to the next department, and then the next if need be. I have only ever seen a phone number for Special Services (which deals with disabilities and special needs), but I am sure they have a TTY or VRS capability...
Again, my experience is with the DL interpreters, but they are all the same company and I have had only the best experiences with them!