There is no good reason that your present ISP cannot give you your MAC code immediately. Its only the ADSL line reference no. Get back onto them and insist you want to know it as soon as possible, emphasise that you wish to migrate and not cancel.
Don't cancel your account though because if you do then you will have to wait for your current ISP to disconnect you then your new ISP to set things up again.
Do use the migration route and as soon as you receive your MAC code pass it on to your new ISP and they will deal with the migration. Going this route you should only be without your broadband for 20 minutes or so why the changeover is made