Bombing the HQ to wipe out radar for an entire country seems like griefing to me. Taking out the country's ability to capture bases is my suggestion.
When the HQ goes down, base capture is effectively stopped until it is resupplied, just like it is now. Troops would still run, but an arena setting would keep them from taking bases until HQ is restored.
This is something even a horded country could do to stave off the onslaught. With ENY limiting the steamrolling side (that is, if ENY would kick in before the high # side has a 25% advantage*), they could not up 163s and a small number of attackers could succeed in flattening the HQ. That could buy the outnumbered side even 15 minutes of respite to regroup. Would be more worthwhile to go that far to get some tangible results, other than "We sure pissed them off!" The low numbered side could also up cheap 163s for defense of their own HQ, making it a tempting but costly target for the steamrollers.
Something like this would also be a great motivator for the hording types to defend if they wanna keep rolling bases.
* Not sure what the percentage is for ENY to engage, but it does seem like the high numbered side sometimes has almost 40% more players and a 0.0 ENY.