Hi Vinod,
You can do an enhancement is event 655 for rejecting those payments for payment method X which have a due date in future. I guess this will solve your issue.
So when the FPY1 run is executed, the due date is set as 31.12.9999, so it is not having any problem for payment method Y. For Payment method X, it will pick up all the items which are due/not due.
Now in event 655, you can exclude the items for payment method X which are not due by rejecting them by comparing the due date with the System Date or the posting date used in FPY1 run.
I am not able to get your second query. can you please elaborate.
Thanks,
Amlan