I am not suggesting my proposal fixes everything. A proposal need not fix everything to be an improvement. If I can get my pick in and go about my day it is better, even if I have to wait for the next round to resume the next day regardless.
Moreover, if an owner disappears for an extended period of time and they come back and find they are the only pick left to make in the round, they can submit their pick and keeper at the same time before they disappear again, thus, in fact, speeding up the turnaround time between rounds after all.