@sarawolk I can envision a natural progression as: (1) implement straight approval, (2) eventually indicate the shortcomings of approval in guaranteeing election of Smith set candidates, (3) reform to include a ranked primaries to restrict to the Smith set before the final approval vote.
I agree it is not feasible to implement the kind of change needed for the mentioned kind of system all at once.
If approval were established somehow, the (rational, IMO) debate relevant to (2) and (3) would probably be about majoritarianism versus participation and maybe some tactical considerations.
Your point about tie-breaking is fair. For example, why not use Bucklin voting restricted to the Smith set, adjusting ranks to include only those candidates, which is similar to your suggestion. One major reason in that specific case is because it fails independence of clones.
I’m not necessarily just after a simple tie breaker. My concern is with reconciling majority cycles, which can destabilize the system. Something like approval in a second round enables the competing majorities to compromise more directly with full information. Otherwise a true majority may feel jilted by an arbitrary tie breaking rule.