Good news - looks like that's now fixed. I'll get that pushed out in the next update (in the next few days, once I fix the other bugs that my ill-fated Kaiserreich test revealed).
In the meantime, I've run your save and mod through the converter, and attached the output to this post.
(With one small difference - the Vic2-to-HoI4 mod didn't have any ship names, because my ship-name-conversion code for the Vic2-to-HoI4 converter hasn't made it into a release yet. So I've just edited the Stellaris mod to use the newly-released Roman name list instead. It seemed appropriate!)
Thank you so much ^.^, I've been fairly excited to try out this converter ever since a friend of mine showed me a post on reddit about it.
Nice touch with the name list to. I'm looking forward to seeing how far this converter goes - I did see that you were considering a Hoi4 to DEFCON to Stellaris converter, which is crazy, but in a good way.
Edit - The only 'gripe' I have (if any at all) is that the ruler's family name is no longer 'Pendragon' (It's a really small gripe, I know, and I've already fixed it in the save file), this is the same family I've kept going, maintaining massive amounts influence in the Empire's politics since 476 (And I've made triple sure that all children are 100% Legitimate! A harem of lesbians made sure of that!)
And, another thing, this one is more of an idea than a gripe, but why not have an option(s) of determining the 'history' of the convert yourself? Lets say, I conquer the entire world, every last little region, and with 'early' space exploration I sent out a colony ship (almost like the regular Stellaris lore with the Commonwealth of Man), or perhaps a couple ships, and they can be competing Corporations, or colonies from competing family members (of the dynasty currently ruling Earth) Maybe having a couple going rouge and going full Democratic, or one Communist. Either way, there's a lot of fun ways you can go about this ^.^