Also, your other suggestions seem to indicate a sort of hack to the file, either modifying the IDML, or modifying the INDD, but either way it would seem that any further updates to the file, and hence updating the cross-refereces, would remove these, yeah?
Yep! I guess that wouldn't work for you, in that case.
Some pictures or sample files would be very helpful, here. I'll keep guessing, though.
I'm imagining that you're working with a client's file that maybe didn't see a lot of pre-translation file engineering before the PM dropped the IDML into your TM tool, right? If I were to be given the task of pre-translation file engineering and I saw that there were a bunch of figures with capital-C Captions, be they Live or Static, or using text variables, or paragraph numbering, or something else that is not directly editable, I would say "Hey Client, what are the target languages for this project?" And if the answer included any language that used case termination on nouns (or any other fancy syntax that doesn't map well onto English grammatical structure), and that perhaps had auto-generated xrefs in the body text, I would
immediately
replace everything with editable live text. Only then would I say "Hey, Client, I had to blow out all of your auto-genned captions due to the complex grammar of your target language(s). Do you expect to... y'know... be able to add or remove figures and have numbering auto-update?" If there answer was something along the lines of "well, yeah, Joel, and the metadata content as well, that's why were are using Live Captions" then I would go and rebuild all of those captions using number-only xrefs to do the auto-numbering. That way, their numbering can still auto-update, using the only real body-text-friendly auto-numbering tool that InDesign has. Then I might leave verbose, detailed notes in the pasteboard so that when the original designer got their file back, they'd have some explanation as to why their carefully managed document interactivity has been removed and replaced with a bunch of manual work.
These tools in InDesign weren't designed with Interesting Languages in mind, I think. There are lots of advanced features in InDesign that work just fine in English, Spanish, French, and German (maybe Japanese if you're lucky). Other languages, not so much. The vast majority of my work is in these Other, Interesting Languages, which is why I know so little about how these tools are meant to work. If I come across them, I only know that I need to remove them entirely and replace them with text my translators would see from their view inside the TM tool, or my 30-language job will fail on e.g. a table header in 20 out of 30 languages. I learned this mostly by being in your shoes, at what I thought was the end of the project, and finding out that I had hours of fiddly manual work yet to do. Apologies if this feels disrespectful or flip, but be thankful it's only two languages, not twenty!
The foregoing is true of text-variable-based auto-generated text as well, such as Running Headers. If it needs to be in body text in a language with case termination (or three or four other syntactically complex circumstances), there's no way to use InDesign's text variables. Translators don't see that text in their view inside the TM tool. It has to be done manually.
How do you go about inserting “Figure ” at the beginning of an auto-numbered paragraph?
Many years ago, I used Jongware's IndyFont to make a single-character font with the entire word "Table " in.... Burmese, maybe? Lao? as a single glyph, so I could use it as a bullet character, in a similar workflow. It was a dirty hack, most likely best left in the dustbin of history. But it did make figure-numbering automation possible.
Even though it's been years since I did any serious work in Framemaker, I still encounter these situations on a regular basis, where I long for a feature that we've had in Frame for decades. InDesign's long-document features are often weak, in comparison with Frame. If you're coming from a Frame background, get ready to rebuild a bunch of stuff manually, and feel like you're wasting your time. For what it's worth, going the other direction has much the same effect: "Oh hi, here's another graphical element that'd take me ten seconds to edit/recreate if I were working in InDesign, but I'm working in Frame, so I guess it's time to reopen Illustrator for the upteenth time this hour!"
Lastly, I do encourage you (at some point in the future, when you have the leisure to do so) to go post this at the Uservoice. If you scan the suggestions there, I assure you that you will find a bunch of other feature requests for things that are very familiar to you from Framemaker, and if you upvote those features then they will have very slightly improved chances of being seen, and perhaps implemented, by the development team.