I doubt that offering said players new contracts a few weeks ago would have made any difference. Put yourself in the players position, either he is happy here and wants to stay which ever division we play in or he will not sign at that time because he wants to see if we get relegated, then he will leave if he wants to continue playing in division 1. In any case it makes no sense accepting the clubs first offer, better to wait until the season ends to see what other offers you get.
Maybe, maybe not, but I guess there’s no harm in trying though. A couple of Stevenage players signed new contracts recently.