[Avodah] Cohen demanding a sold aliya

[Ben Waxman via Avodah]

My Friday night beit knesset sells the Shabbat morning aliyot right 
after kabbalat Shabbat. In this beit knesset, none of the members are 
kohenim. Were a cohen to come to the beit knesset on Shabbat morning, 
would his right to the first aliya (the right not be embarrassed) over 
ride the sale? I would imagine no, a sale is a sale. Plus, why should 
the beit knesset lose money?

If the cohen says "I am willing to pay whatever the Yisrael paid" would 
he then have the right to claim the aliya?

If it matters, the beit knesset is Yeminite.

Ben