That's what I started to do, might send the second wave of offers later
I make a game of it, see if I can get through the whole list of trade partners before someone accepts. More often than not I get an acceptance before I run out of people to send offers to.
I got the flu all the week so I was not able to log in and to try to "sell" my players, so just a message to remind that I sent players on the trade block, and that I don't ask a big price in return, I just don't want other players as I would like this to help me to bring my roster to 53 players...