Got your private message. The good news is that the 11SM you are talking about depends primarily upon elevation and intervening terrain since getting planes on the ground from ten miles line of sight is not a problem, at least not a problem as relates to affordable, available technology. I glanced at the frequencies involved and a custom 4 element, 10db yagi would do it for you depending upon whether that one APP channel up around 134 is transmitting from the field or not, and even if so that yagi could be broad-banded at a loss of about 2db and still probably do the trick. . . again assuming line of sight or close to it, say, skimming the treetops.
I am in the process of setting up a back-up feed for JFK from a distance of 8 SM with a broad-banded version of the 4-el yagi running at 45 feet AGL and delivering between 7 and 8.5 db from 121 to 130, and our preliminary testing is pulling in just about all the stuff on the ground including some walkie-talkies and tugs as well as planes sitting at the gates in and around all those terminal buildings, the toughest stuff being at the far side of the field (and buildings) and an additional mile away. Even a broad-banded omni-directional sleeve antenna ten feet above it (about 2db gain over a ordinary ground plane and on its worst day equivalent to a perfectly configured j-pole) was getting about 90% of the ground traffic, but the yagi filled in the gaps and made things solid. And that's with 4+ db loss in the 100' rg-58 cable run and no amplification (yet). But that path is at tree-top level so your results may vary.
The path analysis is the key because it may not be feasible to get a six-foot yagi above the trees whereas getting a sleeve dipole or your j-pole might be. On the other hand if above the trees is not possible in any event or there is intervening terrain the only way you are going to pull it out is with a strong array. As a rough rule of thumb you gain 3db for each doubling of elevation once you clear the trees, meaning it is not going to get you anything additional once you get that lightning rod above the squirrels, so the first thing you have to decide is if you can go that high. If trees are not an issue anyway because you live in the clear, than it is a no-brainer to go with a yagi as the only difference in signal that any additional elevation above roof-top will get you will be less noise from the blender in your kitchen, and that's only if your feed line is properly de-coupled.
One thing I can assure you... if you stick that j-pole at roof-top level and ground signals break squelch or can be heard to any degree at all within the noise, you will be able to pull them up to usable levels with a reasonable effort.
If you are handy and want to build your own antennas as I do all of mine, I'll be happy to model the dimensions for you once the requirements are known. I'll send you a photo of the JFK stuff. So get out your sectional and topo maps as well as Google Earth and get to work!
I just want you to know, Striker, we're all counting on you.