So I figured out what the problem was... and as always... it was me.
I've been trying to use a modular table file to try and make all of the changes in one easy to move file, that I can just swap from one folder into another, as the mod gets updated. Unfortunately, while modular table files allow you to add or replace things from the original, they can't remove something (as far as I can see), so I've been forced (reluctantly) to edit the included ships.tbl file, and comment out entries for subsystems no longer present. When I got to the Gigas, I forgot that the newer one, having in excess of 100 turrets, starts naming them with 001, rather than 01. At first, I simply commented out some of the upper entries in my modular table file, so I could at least load debug FRED. Then I looked for things I'd missed, like glowpoints, textures, missing MOI, or anything other that the debug would warn me about when I placed a ship on the grid. During my test of the Gigas however, it mentioned not finding 'Turret01', and that's when it hit me... I had to comment out all of the turrets in the ships.tbl file, because it was trying to load all of the 2-digit ones from the table file, and the 3-digit ones from the modular table file, and that was exceeding the limit. After fixing that, I was able to uncomment-out the ones from the modular table file, and it loaded without issues. As I said, it was me. When I'd used it before, I simply made my changes directly into the provided ships.tbl flie, rather than trying for a modular one. Oops.
Anyway, now I can go on to try and import some of the Uber-detailed models from the EA pack. Wish me luck.