I have been in your situation and I think that you should do nothing. Your children are old enough to have their own opinions and make their own decisions. Anytime you do or say one way of the other will end up being thrown back in your face.
The more you get involved, the more your ex will put the blame on you.
There is no rush here, it is not the kind of situation where teens are making irrevocable decisions. Perhaps they just need some time and space to come to terms with what’s happened and work out what THEY want. Their dad will still be around if they change their mind in a few weeks or months.
Id step RIGHT back and tell the kids that it’s up to them whether they see him or not, you will support them either way. That no decision is permanent , they don’t have to commit to anything . They can make a plan for the next few weeks / months and then review it.
They can try no contact, low contacts, texts only or perhaps one or two zoom calls a week . It doesn’t have to be face to face if they don’t want that.
With most teens, the more you push, the more they back off.
Tell them it’s ok for them to take some time to decide and to tell their dad that’s what they need.
You need to give your 16 yo permission to tell his dad that he will no longer be a go between. And that if his father doesn’t respect that boundary , he may need to make other choices.
I had to tell my kids very firmly that they had to respect their siblings privacy, as the one who had contact was giving dad info about the others that they didn’t want shared. Ex was then using that to pretend to his friends and family that he has a lot of contact with all the kids , which wasn’t true. In his case, he didn’t care about seeing the kids but he REALLY cared about how bad it looked on him.
I would defo NOT try to do the “ he's a great guy really , remember the fun we had “ routine. I’m sure your kids are not stupid and they will see right through your attempts to Manipulate and guilt trip them. They’ve had enough lies and dishonesty in their lives from their father, they don’t need it from you too.
You are not your ex husbands PR person, your only responsibility is to your kids and what’s best for them.