You can normally safely put much more voltage (often anode voltage) on G2 when a tube is wired in triode configuration, in general anyway. The close anode voltage minimises the dissipation of G2 - the anode collects most of the electrons and takes most of the dissipation.
The problem comes in pentode or UL mode (your intention I think). This can cause the voltage on G2 to be significantly above the anode voltage during parts of the cycle - that can increase G2 power dissipation a lot (electrons are attracted by G2 preferentially), hence the much lower voltage limit.
EDIT: That's the problem with your UL / Triode switch anyway. If you want to know what voltage you can safely put on G2 in Triode mode, connect it to the anode via a milliameter, measure the G2 current and calculate it's dissipation. As long as it's below the limit (3.2W?) you should be fine at that anode voltage. NOTE, also check the pinout - you may risk insulation breakdown if G2 is higher than normal (the Anode is on the top cap, G2 pin is next to a heater pin!)
EDIT1: To cut the story short, you ought to be able to use more than 350V in triode mode, but not as high as 700V.