I believe your problem is a temporal (earthly) versus infinite (heavenly) one.
On earth we are bound by earthly laws, ie. time marches on, so little time, not enough time, no time.
In heaven, where the Infinite reigns there is no time, God, Mary and the saints don’t get overloaded by prayers to them. They all exist in the eternal NOW and experience all past, present and future as NOW.
Therefor they have all eternity to hear and intercede for us.
This is the same reason that the Catholic Church re-presents the Christ’s death and Life at the Consecration of the bread and wine into His Body and Blood - Christ is still being sacrificed in Ininite time in heaven (real time to us mortals)
Regards,
Lurking’
Ininite = Infinite
Thank you all for your helpful responses ... re: Mary and the saints entertaining thousands of prayers at once. I do not agree with the doctrine of prayer to men and women in heaven, but I agree that this point would not necessarily be an insuperable objection to it.