Is the food still being eaten? Is the litter box still being used?
It seems to me if the answer to these two questions is NO, then searching the house may be a big waste of time.
The cat ate food and used the litter box last night.
We're having trouble finding it today.
Being missing since 3:30 this morning isn't really that long. They can go without eating... without using the litterbox... that long. I bet it has not escaped if you've been careful about doors... but remain vigiliant about keeping doors and windows closed.
I think the cat's just stressed out, some cats don't transport well, and all the rummaging around looking is probably not helping. I'd calm down, let the house be quiet, and you'll see the cat come out eventually.