The way I see it, they nominated Hindenburg, because no one else had enough prestige to stand a chance against Hitler and unite disparate forces you just mentioned. Hindenburg was a powerful symbol.
Even if they did nominate an alternative candidate, it would probably result in a second round of elections. The point is that the Germans were tired of elections. If a 'sane and healthy' president didn't offer mandate to the Nazi's, in all likelihood a new parliamentary elections would result. Again.
Even with Hindenburg it resulted in another round, as he only got 49% in round 1.
If the Germans were tired of elections, why were they turning up in so huge numbers ?
Also, lastly, in the november 1932 elections, the nazis lost 34 seats (~4% less of the total vote share), which might indicate that support for them was falling. On the other hand, Hugenberg's DNVP, having backed von Papen in opposition to Hitler in the political fighting that took place in parliament, gained 15 seats (2,43% upswing).
Come to think of it, the situation is so volatile it could probably go any number of ways.