Branding effects are not the core problem, they just make the core problems worse.

CORE PROBLEMS:

A system that continually converges down to only two viable parties, rewards divisive candidates and handicaps broadly-liked third or fourth party candidates.

A system that allows one party to capture all three branches of government. Incentivizing extreme power plays/centralization in and between parties. (Usually starts within a party.)

A system that lets parties integrate at Federal and State levels, suppressing or eliminating the otherwise strong benefits of Federal/State government decentralization. Creates massive incentives for out-of-state capture of state politics.

A permissive system for players to cache out as system-undermining lobbyists after a tour of "service".

CORE SOLUTIONS:

Maximum seat-run limits for parties, forces cross-partisanship and coalitions as some level. Any is better than none.

Separation of parties at Federal and State levels. And/or limits on numbers of states a party can operate in. Use the Federalized system of decentralizing Federal/State government to achieve parallel decentralization of parties.

Take money out of politics. Hard to do perfectly, but any limits make a big difference. Brands operate on pervasive non-rational visibility and repetition, i.e. money.

Voting systems that give wide-appeal candidates an advantage.

Voluntary acceptance of a post-tour lobbying bans, as a requirement for political and policy appointments. Remove that pervasive conflict of interest machine. Disincentivize game players from public "service".