I have been in your shoes loads of times in the past now it's mostly 30 mins after Bt and of course I have to change her bum. I havn't been able to leave LO in a poopy diaper as she has very sensitive skin so what I do is bring in diaper/washed out warm wipes and bum cream. I change the bum In the bed I just lean right in there ( mind you , lo bed isn't to deep and I'm almost 6 feet tall with longer then normal arms). If you cannot then pick him up and lay a soft blanket on the floor and change bum there as fast as you can, then do a rock/snuggle and lay back down and remember No TALKING lol
HTH