Ok, I quickly scanned through the macro's. Most of the macro's weren't that interesting at all and quite simple. One was a bit more complex and I haven't studied it thoroughly yet, that is
Voir_NomsPropres_et_JeuDeCaracteres. From what I gather due to the quick scan, I assume it does some stuff in fixing names and titles.
Your actual process and intentions are important for the next step. My answer would depend on your process. I will make some assumptions and work from that. If the assumptions are not correct, please let me know.
1. You want to process one or more of the macro's and are not interested in the layout offered by the macro. With layout I mean the Styles and such.
2. You do want the marking of wrong words and perhaps the other fixes (convert hyperlinks to endnotes?)
Now, if these assumptions are correct, I understand the issues you are facing. In my opinion it has
nothing to do with the handling of ODT by Word, but more that the macro's are combined with a template.
Now, for a possible solution. Most of the stuff, especially the macro
Recherche_erreurs can easily be handled by my add-in. In fact, I think my add-in would be better (

). It is just a long list of searches and marking (color red) of each hit found. It just marks all the words that might be wrong. That option is in my add-in and if you have known fixes, you might want to use the S/R procedure of the add-in. Of course it will take a while to put all the searches in it, but it is not hard and
you can control which goes in and which not. You have control, not me. Adding a marking/search is easy enough and is not hard-coded.
My add-in will not change your document any more than that, if you want. It will leave your styles alone. Also, I saw some macro's that might influence dialogues. I want to put your attention to the
Check dialogue procedure of my add-in. It should be able to handle that macro as well.
In short, I think that my add-in would be able to handle most parts of the macro without a hitch as long as you don't need the Styles in the template. Some others not, but I do not know how important are those. If they are, I could integrate them with the add-in, they are not that difficult at all (with the exception of the one mentioned earlier, I didn't check it yet).
Now, it sounds like an advertisement for my add-in, sorry about that. But I feel that it could cover most of your wishes already. The marking function is something I build in by request of BetterRed and it seems that this is also the core of your macro.