I never played with this before, but I would suggest that you
lock) the version of the dependencies that cause you trouble. This way
apt has a more limited number of possible solutions, and perhaps doesn't get confused when you attempt to downgrade the other packages.
If nothing else works, you could take the manual approach suggested in this answer: How to Downgrade a Package via apt-get?. Basically, download the necessary
.deb packages manually, then install them one by one using the lower-level
dpkg and one of its forceful arguments:
--force-depends-version, or even
In the same spirit as the above, you have the
downgrade(*): Install a package, even if newer version of
it is already installed.
Warning: At present dpkg does not do any dependency
checking on downgrades and therefore will not warn you if
the downgrade breaks the dependency of some other pack‐
age. This can have serious side effects, downgrading
essential system components can even make your whole sys‐
tem unusable. Use with care.
But this assumes that you've read
man dpkg, and that you understand what you do:
Warning: These options are mostly intended to be used by
experts only. Using them without fully understanding
their effects may break your whole system.
See Error: version number does not start with digit and How to install an older version of Java and How to install a older version of package like liquid 2.2.2? for examples of:
sudo dpkg --force-downgrade -i your_mesa_package.deb
And see How can I install a package without installing some dependencies? for an example (along with the appropriate warning) of:
sudo dpkg --force-all -i your_mesa_package.deb
Yet another approach would be to create a dummy
.deb package using the
equivs package (and perhaps a slightly different name). Then installing the dummy package should allow you to remove the "true" package while keeping the relevant deps, and then install the older version. I'm not sure how exactly this would work, but check this relevant thread for details: How to remove a deb without removing its dependencies.