Triggering PSRSYNC under the GTCCR register did the trick for resetting the prescaler and getting consistent timing results. Unfortunately while researching that this morning, another thought plopped in my head that could be a potential deal-breaker.
The entire concept was to have the transponder send a signal and the receiver to bounce one back, incurring a delay due to the distance between the two. The problem is that you're still relying on the system clock to get around to acknowledging a signal has been received and responding back. Any delay between the data received interrupt being triggered and the microcontroller registering it completely nullifies your ability to accumulate that delay.
To give an analogy, it's like giving your friend a call, but they can only answer the phone at ten minute intervals (IE 5:30, 5:40, 5:50). As far as they know, they received the message at 5:50, but you could have sent it at 5:46... Just like the transponder, it can send the message at anytime, but the receiver still has to wait anywhere from 0-62 ns before it can acknowledge it and send another back. You can repeat your call at 5:59, but it's still 6:00 before it gets picked up. No matter how many times you repeat, what delay you created gets reset to a standard interval by the receiving end.
I think what I may have to do is change to sending messages of different lengths and increasing the length until I roll over to the next count of the timer. This way I can attempt to line up the interrupt triggering the moment it can be registered. At that point a combination of the message length and the time-of-flight can be used to calculate distance.
In other news, I'm beginning to like the Leonardo/Micro platform. With the 32u4 chip, there is a high speed timer that can be clocked off the PLL clock... at 64 mhz. Pretty handy as it gets resolution down to 15 ns, but I likely won't use it. Ultimately I want to develop a solution that works on any Arduino platform and doesn't cater to the strengths of just one.