csal, I think you have to run things the way you're already doing, at least certainly for the other team's phones in the banks of 6.
As far as the main line goes, a hunt group may be your best bet, using the new CM4.0 feature of "Broadcast Ring". That way, you add the various staff members phone numbers into a Hunt Group and set it to broadcast ring. A couple of things though - there would be no way to tell the difference between call to the main DDI and a call to your actual phone, other than the sound of 30 phones ringing. Also, not having used CM4.0 yet, I'm not sure if this will even fix your "missed call" problem.
I suppose you could put a new line on everyone's phone with made up (non-DDI) numbers which, like above, you put in a "Broadcast Ring" hunt group. Then at least you'll have visibility on whether a call is for you, or comes from the main line.
The missed call problem crops up for us too - we have about 10 secretaries who have 14 button side cars who look after everyone's line in their dept - they always see missed calls on their phones. Drives them nuts, and so, they drive me nuts...
IPMA stands for "IP Manager/Assistant" and basically it gives you the ability to set up a secretary for a bunch of managers - they get those manager's lines appearing on their phone and you get special features like Intercom and Forward to Voicemail that you don't get normally. Apparently it's quite nice...
Haven't used it myself though, since it hacks all your partitions and CSS's to make things work and we have a really complex parition/CSS setup for our Dealers here - around 250 of each. I haven't had the guts to let the IPMA Wizard loose on it yet.
I'm (hopefully) getting my CM4.0 test lab setup next week and I'll post back if I make any progress.