It might not be for everyone/all types of medication, but I took my progesterone pessaries rectally including when on holiday and I went swimming, never needed a pad, never needed to lay down for it to absorb, it worked for me and made life so much easier!
I was advised that the stuff that comes out is the coating on the pessarys (wax coating) I put them in when I get to bed and then get up and go for a wee and find the wax drips out fairly quickly. Then the morning one i give them 20/30 of me sitting down then do the same and crack on with the day. So maybe set your alarn 30min earlier and do it before you go out for the day?
Apparently they only take like 10/15 to absorb into the blood
I used to set an alarm an hour before waking to insert, then would have a quick shower on waking, then do the second going to bed. Then it never affected my day!