Check out this video:
While their slide isn't exactly like your slide, both are similar in having a "box that makes the slide too narrow for a recliner to fit without tipping forward.
Their solution may be adaptable to your slide and a "plus" for you is that your "box in the slide" is low enough that if you do install recliners, they will already have the clearance for the back to recline without having to pull them away from the wall....
Might work, see what you think.