I think who without Joseph and his son’s Spanish inheritance Max will be much more interested than OTL in Poland. If Max will present his candidature he will have support from France and his mother-in-law and maybe Austria will stay neutral between him and the Elector of Saxony.
The OTL election was won by Conti so here Max also will win and is unlikely who the Elector of Saxony will try to take the Crown by
force here, against a fellow Elector who is also the son-in-law of the previous King and without full support from Austria...
I'm afraid that you are a little bit confused with your timing. At the time when the PLC throne became vacant
Max was fighting against France so why and how he would suddenly get Louis' support? Second, at a risk to look as a male pig sexist

, in 1697 Marie Casimire was not a powerful political figure either in the PLC (out of which her own son immediately sent her to the Rome, anyway, making the whole thing a mute point) nor in France (her ambitions regarding her French relatives being treated as the royals did not find any sympathy from Louis).
When the vacation opened during the War of the Grand Alliance Max was more important to the Hapsburgs as a governor of the Spanish Netherlands than as a candidate to the Polish throne. OTOH,
in OTL Conti won a vote of majority as a French candidate (war with the Ottomans already lost its popularity and for the Polish side was not going to end with any significant gains) so how Max, who was at that time the Hapsburg ally, would fit the definition? Louis could be assured in Conti's loyalty but Max' loyalty was not on the table until the WoSS.
As for his competition with August, an idea is interesting but by the obvious geographic reasons August was in a much better position to march his army to the PLC than Max, who was, anyway, at that time fighting the French in the Spanish Netherlands. Not to mention that, besides rather vague support from Austria, August had a tangible support from Russia: Peter's government had been actively bribing the deputies of the Sejm not to let the French candidate to be elected (which would mean breaking anti-Ottoman alliance) and while at that time the Russian army was incapable of fighting the Swedes, it was more than capable of dealing with whatever was passing at that time for the PLC troops.
Austria in 1697 was still busy with the Ottomans and it is highly unlikely that it would go to interfere militarily in the Polish conflict. OTOH, Peter's Azov campaigns had been already over.
OTL Max had neither the support nor the interest in the PLC because he was pointing everything on his son’s Spanish inheritance. Without that the PLC is likely a good opportunity for him
You keep ignoring the timing:
in 1697 his son was not a heir to the Spanish throne so he could not bet anything on the Spanish inheritance. The PLC was not a good opportunity for him because he was already sitting on two chairs: Electorate of Bavaria and governorship of the Spanish Netherlands and, as far as I can imagine, any of them was more profitable and less troublesome than the PLC.