Well, the IRS is not processing any paper documents right now. So even if you wanted to apply for a new ITIN, that would mean mailing a paper W7 plus a paper tax return to the IRS. I think applying for a new ITIN is going to cause more trouble than it’s worth.
I don’t think there are any important deadlines you would be missing by filing late. You can’t claim certain dependent credits without a Social Security number, and you must have the Social Security number before you file a “on time” return, but I don’t think that applies to dependents who have ITINs. What I suggest in your case is that you file a request for a tax extension. That would give you until October 15 to file a return that would still be considered “on time“. Presumably, the coronavirus restrictions will be relaxed and the IRS will start answering their phones again before October 15.
