Is this the type of unit that you have: SALICRU Series RE2 or PLC2: The specs look excellent. They also can handle high temporary overloads, e.g., even 1000% for 50 ms, so the lamp starting current shouldn't be a problem, particularly since your 600 VA unit has margin over the steady state load of 250 W plus inefficiencies.

It is suspicious that neither fuse seems large enough for 600 VA. But I can't say what to do since I don't understand the role of the two fuses. Perhaps one is for the microprocessor and one for the current that goes to the load? I suggest trying to get a manual for the stabiliser -- try contacting the distributer or manufacturer.

Slow versus fast on a fuse is the timescale of blowing: will the fuse tolerate a brief current above its rating.