@lepea We applied for a normal 600 visitor visa and linked it through the immi account. I can't remember the specifics of the form, but I'm fairly sure that we also made clear that he'd applied for the 390. We asked for a six month visa and they granted 12 months, which was unexpected but good, as it turns out! We're probably going to apply for a new 600 and explain the circumstances (he can go back to the UK but isn't guaranteed to be able to come back, and I'm working so can support us both) and hope that that triggers a look at the 390.
I understood that family of citizens and PRs are allowed into Australia (there's no grounds to deny them) but you do need a visitor visa to be able to come - I wonder if what they were referring to in their email was the fact that you didn't have a valid visa to enter (390 or a 600) and so couldn't be allowed to travel? From what I've seen on here other people are using 600s to get into the country. I would be surprised if they didn't give you a 12 month visa and once you're here, it would be very tricky to refuse a subsequent visa or try to send you back to the UK given you have children who are citizens. The only downside is the cost - it's about $300 for the visa application, which is a lot if you're not certain. I think it's worth a shot, though. I can't see how they'd refuse it, particularly if you need to be in Australia for personal reasons with your husband and children.