The NXP-Converter pretty certainly won't work, indeed.
You might be able to do a step-by-step conversion manually. If I want to convert one of my Lemmicks levels to the newest version of New Formats, I have to open the level in the latest Old-Formats editor (10.13) first, save it, then open that file in an early editor of New Formats (e.g. 12.6.5), save that one, then open the New-Formats file in the newest editor (12.9). Doesn't sound like much fun though to do that manually for every single level.

Also, I remember playing GigaLems in version 1.43 - which, among others, had no clear-physics mode - so any instance of a hidden trap or exit caused real, actual trouble. And if I get annoyed by those things, that means something, since I have quite a bit of tolerance for them.

When GigaLem was a guest on Arty's LP of SEB Lems, he even mentioned himself that he made IchoTolot ragequit with this pack. As far as I understood his comments in that LP video, he has moved on from hidden objects and is now quite a strong opponent of them. (Arty argued in the LP that the existence of clear-physics mode makes them more tolerable now than back in 1.43, but GigaLem said you shouldn't have to use CPM in the first place, which is a position a lot of NeoLemmix players share.)
Thus, I assume GigaLem's view on this early pack of his is a similar to the one I have on my own first pack (Paralems) - which I'm not planning to convert either, except for a few select levels.
In short, I wouldn't hold my breath for this pack being converted

. Even though I did enjoy some of the puzzles very much and would be happy to see them brought back in a New-Formats pack. Maybe as an additional rank (like the MegSEBytes rank in SEB Lems), or as a selection, like in Lemmings Redux.
@GigaLem: I hope I did not misunderstand and consequently misrepresent your position here, so please correct me if I got anything wrong. 