I'm sorry but I have to disagree with everyone above. If you know what your bottom line is for moving then as long as someone offers above that you might as well accept instead of all this fannying around making people wait 24 hours.
I can't understand why your EA shouldn't know what your bottom line is, the more money someone offers the more commission they make so of course they will want the highest offer they can get.
Your DH will have to go in January, if you haven't completed by then because of delays or a chain, what will you do?
Will you go with him into rented? Will you stay behind and do the whole single parent in the week bit?
Any messing around for up to a week making people wait 24 hours massively delays your move. Then hopefully karma kicks in and you are made to sweat it out while someone does it with your offer. Bear in mind all the closed offices over Christmas and New Year.
We lost the house we wanted by 1 day because our buyers didn't come back with their next offer which they now have done. This means we now have no house to go to. So it holds everything up.
My advice is don't mess around, any offer below what I wanted I would immediately tell the agent they need to increase their offer. When it starts getting close to where you want them to be, name your price slightly above what you want, then their counter offer should be at your bottom line price. Or you may get lucky and they are way over
Good luck. I was left behind in a house waiting for all the paperwork to get sorted with the solicitors while my DH lived with his parents for 6 weeks I did the single parent bit and it wasn't nice. We completed and moved but it was stressful.