Luck, and barring that, perhaps enough money to buy a new power transformer.
The 5U4 filament winding draws more current than does the 5AR4 (3.0 amps vs. 1.9). The stock Stereo 70 power transformer is marginal to begin with, and hanging more filament draw on it can't help its longevity. Also, do the filaments of the tubes on that aftermarket board draw more current than two 7199s? If so, there's another added strain on the already-marginal power transformer even before your rectifier substitution.
Also the 5U4 "turns on" faster, as you noted; before the filaments of the tubes have warmed up, you'd be throwing B+ into the tubes. There has been controversy about whether this is actually harmful to tubes (some say it causes cathode stripping which shortens tube life, others say it does not) and Dynaco did use the 5U4 in its Mark II power amplifier.
The 5U4GB also has a higher series resistance than the 5AR4, so the resultant rectified B+ voltage will be lower, and your amplifier's output power will be reduced.
Now, WHY do you want to substitute a 5U4GB for the 5AR4?