I have an initial version of PyRun for Python 3.10 running as well.
This created a few more headaches in order to make it work with
setuptools and some glitches which appear to be bugs in 3.10
(https://bugs.python.org/issue45563 and https://bugs.python.org/issue45562).
Nothing major, though.

I'll have to check my version of the freeze tool against the one
in Python 3.9 and 3.10 to see whether there's anything in the
core versions which could cause the tool not to work.

BTW: (My) freeze.py uses this startup code as main():

int
main(int argc, char **argv)
{
        extern int Py_FrozenMain(int, char **);

        /* Disabled, since we want to default to non-optimized mode: */
        /* Py_OptimizeFlag++; */
        Py_NoSiteFlag++;        /* Don't import site.py */

        PyImport_FrozenModules = _PyImport_FrozenModules;
        return Py_FrozenMain(argc, argv);
}

I still have to dig through the changes you have made, but this
suggests that it replaces PyImport_FrozenModules completely
with its own version, so the default freeze that you are
implementing gets overridden.