... at it's end Polish monarchy was to become hereditary, with the 3 May Constitution ...
With Napoleon promoting the grandson of August III, the aforementioned Frederick Augustus I to the title of Duke of Warsaw in 1807. The daughter of the latter, Maria Augusta, was earlier nominated by the 3rd May Constitution of 1791 as Infanta of Poland whose husband was to become the hereditary King of Poland (the Constitution uses the term "King of Poland" only without mentioning the term "Grand Duke of Lithuania" alongside as it abolished the dual character of the Polish_Lithuanian Commonwealth) if Frederick Augustus had no son.
Frederich Augustus had indeed no son and Maria Augusta never married, so the House of Wettin has no legal claim to a Polish throne, if any such is re-created, on the basis of the 3rd May Constitution.
We are bound to be a Republic. God save the (British) Queen!
And yet, the Constitution goes on declaring the right of the Nation to elect another House after the first dies out! And as the initial House did indeed (by the understanding of the Constitution) die out, we still have the right to elect another House
(not a King! - this is the great difference to the former rule of electing kings) whose members will become hereditary Kings of Poland. So - I should think - anybody can go for this contest, just as for the Eurovision Song Contest, but only if they are members of a certain House
.[Dla czego Marię Augustę Nepomucenę, córkę elektora, za infantkę Polską deklarujemy, zachowując przy narodzie prawo, żadnej preskrypcji [żadnemu ograniczeniu - Z.] podpadać nie mogące, wybrania do tronu drugiego domu po wygaśnięciu pierwszego]
God save the (Polish) King!
It should be noted that the Polish throne was never abolished 200 years ago, but re-shaped to become hereditary.