On a Milan fan's standpoint (my standpoint) I don't think we need to rush things just by qualifying into the Champions League next season. Because to be honest being a fourth, thirds, or even in the second spot of the Serie A table right now doesn't show any good competitive advantage when it comes to the Champions League. If Milan rush things just to be qualified their next transfer window would be a mess for them trying to overspend on everything just to somehow "improve" their chances of winning some games in the CL.
Overspend is an unavoidable and terrible issue for giant clubs when they try to come back as fast as possible, in rush things like you discussed. Look beyond the Italy, in Europe, recent seasons, we have Manchester United. They bought superstar (Pogba), youth talents (Bissaka, Daniel James, etc.), very normal, average defender (Harry Maguire) at very expensive transfer costs. It's unbelievable to see they bought those players at such overvalued prices. Milan should avoid this approach, I agree with you.
Serie A will continue with closed stadium, the show must go on.
Playing matches in closed stadiums don't protect players and clubs' staffs. If one of them infected with the virus, it will be spred out very fast over clubs, and over nations.