I'm not sure what you mean by "lack of a required profile" -- do you mean some sort of login?
But the short answer to your question is that either (1) a plugin/module for Weblate or Transifex would need to be written to get them to understand Rockbox's language file format, or (2) Rockbox's translation tooling would need to be rewritten to utilize a format that Weblate or Transifex already supports. Oh, and the latter would require converting the existing files too.
Either way it's a substantial amount of work, and we're not exactly swimming in volunteers that are willing and/or able to tackle either approach.
I should point out that Rockbox's language files are more complex than (eg) gettext po files, because for a given phrase ID, the "display" vs "voiced" translation can be different. To further complicate things, the same phrase ID can be different on a per-device basis (such as button names or hardware-dependent features). I'm not sure any "standard" translation format can really map to what we need without a great deal of (IMO pointless) rework and bug-reintroducing churn, so realistically (1) is the way to proceed should someone be suitably motivated.
Now that said, I do think getting weblate/etc hooked up would greatly help with rbutil, which utilizes standard QT .ts files. But that's a separate discussion.