I think you may have overlooked an important fact. When rating a fluorescent fixture you need to look at the ballast itself (not the lamps) - it will list the normal operating current required to run. You must then remember that things such as ballasts/electric motors have an inrush current many times greater than the running current - as much as 5 times the normal load with some ballasts.

A 2 lamp 8' HO ballast (you indicate 110w lamps therefore they must be HO) can easily require 2 amps just to run. That would be 6 amps (3 - 2 lamp ballasts) running load on a 5 amp filter - clearly an overload - but once you allow for inrush (some ballasts, as mentioned, draw as much as 5x at startup) you are anywhere from a couple amps over DOUBLE the rated load to as much as 10X the rating.

I am not implying that you do not know how to handle electricity - the fact that you own a clamp meter (or even know what one is) should put you above the average homeowner in that respect but it seems that many knowledgeable individuals do not know enough about things such as inrush/locked rotor current.

Edit: I thought that I should add that even with a clamp meter it can be difficult to actually measure the inrush current unless the meter has fast min/max logging and you know how to use it correctly.