I hope you'll be able to share your findings with us, even if they're negative. As someone who has no stake in Heroku, i have the luxury of finding this problem simply interesting!
My hypothesis is that tenant-specific intelligent load balancers would be plausible; i would guess that you would never need more than a handful of HAProxy or nginx-type balancers to front even a large application. Your main challenge would then be routing requests to the right load balancer cluster. If you had your own hardware, LVS could handle that (i believe that Wikipedia in 2010 ran all page text requests through a single LVS in each datacentre), but i'm not sure what you do on EC2.
However, "hypothesis" is just a fancy way of saying "guess", which is why your findings from actual experiments would be so interesting.