The easiest solution, meaning the least amount of work, which may not be ideal, is to block the IR receiver of one of the TVs so that it receives no input at all. Then you manually turn it on/off when needed and all tuning/control is done from the DTV box for which you can assign IDs.
The next easiest and the least amount of hassle in the long run, is to replace one of the TVs with a different brand. The drawback is that they won't look the "same" if that's important to the installation/decor.
Beyond that, a simple repeater system with blasters will not solve this problem since all IR commands will still be repeated to all devices. Examples of this are simple Xantech (and similar) repeaters.
The complete solution needs a system capable of routing, which means most commonly a remote with RF and an RF to IR base station. The routing means you can send commands to specific IR ports which are then connected to specific devices. URC Complete Control or Home Theater Master remotes with an MRF base can do this easily.
If the DTV boxes have IR blaster ports built into them for controlling an attached TV, this may also work as a routing system. It depends if they have the capability to pass commands sent to them over RF back to the TV. I know that Dish remotes are "universal" and can send IR directly to TVs - which won't solve this problem. Check the back of your DTV box and the manual.
Personally, I'd just stop watching Football and get rid of the extra TV and DTV receiver completely. :)