But that's almost exactly how the US started out (officers were and are elected by their houses, not by the party), and there were well-developed parties by the end of Washington's presidency. Everything you mention came about after the two-party system was well-established.That could work.
However, I think one of the best ways to encourage multiple parties is to simply make it law that the government refuses to acknowledge parties altogether. To me this would imply:
- The government makes no reference to parties on ballots and will put anyone on the ballot who accrues enough valid signatures (whether that's 3 Republicans, 2 Democrats, or whatever). The parties can exist and push their people, but all they are to the government is a group submitting signatures.
- Congress is not run with any respect to parties.
-- Members are seated (and assigned offices) randomly, by seniority, or by last name -- NOT by party.
-- There is no recognition of things such as 'minority whip', etc. Again, the parties can have them, but no one acknowledges them or gives them special privileges or accord
-- Committees are not picked by parties, but are assigned randomly
- The VP is the runner up in the presidential election, almost always NOT of the same party
It would, of course, help if the networks basically refused to support the system, paid no attention to intra-party debates, etc. They would only cover debates if all valid candidates are represented.
There's a reason every democracy has developed parties, and that's that they are extremely useful for everybody. Any sort of system that involves majority rule is going to need legislators to form coalitions, and the need for logrolling means that those coalitions are going to tend to become stable very quickly, i.e. parties. Given a strong presidency that's winner takes all, you're naturally going to coalesce into two of these coalitions (because a coalition that isn't big enough to capture the presidency gets nothing for contesting it).
Parties are also extremely useful for the voter, especially if limited information is available about candidates. I may or may not know enough about State Representative Candidate Smith's stance on every issue, but I know that he is a Libertarian, and can thus both get a general sense of his beliefs and a more detailed sense of what would happen if his party gained a majority. So these parties (and note that it's basically impossible to "ban" parties as they are extremely difficult to rigorously define; French Revolutionary Parties basically started as social clubs where like-minded members met) would serve a purpose by circulating their lists of "these are candidates we endorse" and "these are candidates we want you to sign the petition for," and people would find them useful.
Eventually, as these proto-parties grew and coalesced, you'd want some means of determining who was on those lists (and thus avoiding vote splitting), so some way would be determined to select who was each party's candidate for a district; you could theoretically have independent people trying to gather signatures, but they'd have great difficulty working against the established headwinds. And voila, you have a party system, growing organically. As long as we keep first-past-the-post elections, each district would end up with a max of two competitive parties (even in multi-party FPTP democracies like the UK, you have very few districts where more than two parties are reasonably competitive; what ends up happening is that Seat X is mainly contested by e.g. LDP and Labour, while Seat Y is mainly between Labour and the Tories, and so forth). Again, given the presidency and its importance, these local parties will quickly coalesce into two national parties. And given enough time, people will say "we have these parties, they aren't going anywhere, we might as well formalize the rules about them" and voila, the current two-party system emerges, despite your conditions.