Einar was out at Beale AFB about 4 years ago looking for expertise and gave a briefing on their plan. Looking at the picture in the article, Fossett is wearing a David Clark 1034 pressure suit. Einar appears to be wearing an older one, maybe a 1031. In any case, these are designed so that once you hit 35,000', the aneroids shut off the flow, and your body basically doesn't go above 35,000'.
There's nothing magic about 45,000. Bruce Bohannon didn't wear a pressure suit at those heights. To mitigate the risk, he pre-breathed 100% oxygen for well over an hour to de-nitrogenate his blood, and minimize his chances of getting decompression sickness (DCS). I'm sure Fosset and Einar did too. The pressure suit really becomes an issue when you hit Armstrong's Line -- 63,000'. At that altitude, the pressure is so low that the nitrogen will boil out of your blood. That's bad.