Great news @crh66.I can only speak for the NAB ones I have; Suncorp, Qantas Premier Platinum and NAB rewards Signature - all applied/approved/bonus points given over the past couple of months. No dramas with those ones... as long as they haven't changed the T&Cs recently.
Side note, you mentioned that you've applied for them quite close together - so no issues with credit scores by the sounds of it? I would've thought that applying too close together you'd get denied?