Remote eglot in local buffer

Hi all,

I've been running the Flatpak version of Emacs on Fedora Silverblue for
almost a year. Since Silverblue is an immutable distro, I install
development tools inside Toolboxes and access files through the TRAMP
backend: opening /toolbox:MyToolbx:/~/Myproject/file.c instead of
~/Myproject/file.c. This works surprisingly well: for instance, Eglot
transparently detects installed LSP servers and runs them without
issues.

However, files accessed this way are treated as remote, which creates
several UX problems:

  - The default directory becomes rooted at /toolbox:MyToolbx:, so every
    M-x find-file invocation requires navigating the TRAMP path when I
    want to open a local file.
    
  - recentf distinguishes between remote and local versions of the same
    file, cluttering the history.
    
  - project-prompter and likely other commands are affected by this
  "remote" designation.

My ideal workflow would be to navigate files locally while transparently
using the TRAMP toolbox backend for compile, eglot, and other commands
that need the toolbox environment.

Has anyone got the same peeves as me and found a solution that works
around these problems?

Thanks in advance.