If you want to say "10:00 every Monday" then say "10:00 every Monday" and accept that what you have is not an unambiguous point in time, nor an integer, but a calendar event that may occur at some time in the future depending on geopolitical changes to the local time zone and the rotation of the earth.

Mutilating all timestamps and network time representations by adding a variable unknown step function (the leap second "correction") in order to preserve the illusion that days are always 86400 "seconds" long doesn't help solve this problem at all.