"t's also not possible to hold elections without parties in some form or fashion."
In our present system we have two majority parties. The leaders of those parties have done everything possible to prevent other parties from gaining power. We have primaries to decide the final round of candidates, and one of them (via proxy delegates) is the winner. Other parties need not apply.
Why not choose a candidate based on their ideals instead of party affiliation? Have an open election. The candidate with a majority of votes is the winner.