You're better off two-up for high speeds than solo with top box, as the top box can act as a large wind sail hanging way out there. With a passenger filling in the space between the rider and top box, the wind flows around it much more smoothly, creating less turbulence and minimizing instability.
The bike itself is stable up to 150 mph or so . . .
As for the overheating, these bikes tend to collect a lot of crud up in between the radiator fins, minimizing the overall cooling effectiveness. It's possible that your radiator is working just OK at normal speeds, but the extra load from high-speed riding is overtaxing the partially clogged radiator.
Some riders have had some luck carefully
using a self-serve car wash to help flush gunk off of the radiator. Very carefully
use the high-pressure wand to clean the radiator fins. It's better to do this from the back, although that's hard to do on the GT without removing body panels.
I also recommend a full radiator clean at every 18K service. You have to pull the radiator to do the valve check, so while it's off the bike, give it a thorough inspection and cleaning.
Some riders have also had good luck adding some metal or fiberglass screen mesh in front of the radiator. This mesh tends to collect the crud before it gets embedded in the radiator fins, and is easier to clean, or just replace when it gets too bad.
That should help minimize your overheating problems.
BTW, when you get Porsches or Mercedes crawling up your šss at 130 mph in the left lane, just pull over and let them by. You'll just pass them right back as soon as you near a city and the traffic gets thick.
'13 Dark Graphite Metallic K16GTLD, 24K miles and counting...
'09 Magnesium Beige Metallic K13GT, 60K miles miles and counting...
'02 Mauve Metallic K12LTC, 106K miles and sold
BMWLT#145, IBA# 366, MOA# 111996, SCMA# 24032
All lower 48 states plus Alaska on the K13GT in two weeks . . .
Some people see the gas tank as half empty. Some see it as half full. All I care is that I know where the next tankful is coming from...