Does any FOSS package ecosystem have a good solution to this particular set of problems?
I know Go has historically done something interesting with selecting the "minimum viable version number" for each dependency, but that's the only relevant idea that comes to mind.
With PyPi, at least it's relatively trivial to self-host a pypi instance and self-manage dependency updates.
In the Python ecosystem (vs e.g. Node), at least the total set of first+second-order dependencies for most normal projects is quite small (e.g. medium double digits to low triple digits). It doesn't feel too painful to manage that magnitude of upgrades on a monthly or quarterly basis.