Thanks for the replies.
I checked the doctors I/my kids have seen and their plan participation is the same whether I look through the MD state exchange, ehalthinsurance.com, or the insurer site directly.
So I decided to try going through the exchange now to hopefully make it easier for next year. After about 3 hours of fiddling, I decided it would not allow me to get different policies for myself and my kids, so I tried to enroll only myself. Supposedly I will be getting some enrollment package in the mail.
On ehealthinsurance.com it was easy to do one kid at a time and enroll each one in his own policy. So I did that, but got an email saying I have to upload proof of my qualifying event (i.e. termination of my current insurance). Of course, I don't have that yet, so I guess I will not be able to get this done until after my old insurance is no longer in effect and they send me some notice about it (naturally, the HR person is on vacation until 8/3).
Regardless, it looks like I will have no coverage for 2 weeks because my employer insurance stops 8/15 and the only choice for a starting date for the new policies was 9/1. I guess if something happens during that time, I can pay COBRA after the fact....