I apologize for @DGSketcher 's understandably terse response. Of course, all discussion here is free and hopefully someone can give you some suggestions, however issues with license management are typically a topic for technical support, which is included in the annual subscription fee and is not offered here, but through the distributor/reseller from whom you purchased your licenses. It is, though, pretty unusual to hear of an office with many licenses that is not on a support contract of some form.
By trial/error or pure luck, someone here may know if a fully imaged / cloned disk will be recognized as the same license by the license manager. If I were Graphisoft, I would have tied the floating license to a hash key of the target computer which includes the disk serial number etc and so I would not expect a clone to work...otherwise people would be selling cloned disk images on the black market for Archicad licenses.
If your licenses are all used by the same people or the same physical location, you could consider purchasing a physical Codemeter keyplug (a USB A device) if Graphisoft still issues those. I still have mine from years ago and haven't converted to a digital / floating license because the physical keyplug serves my needs. Contact your distributor/reseller.
As far as I am aware the software license keys distribute files across the whole system. I know if you perform an OS update and don’t upload the software key first it can become damaged. The hardware keys are also copy protected so they cannot be copied or backed up.
The Graphisoft Forward agreement (support) offers included protection for lost or damaged keys. If you don’t have a support agreement it is suggested they are insured against loss or damage.
I don't have software licenses, I prefer the physical key so I don't have a problem with a lost license if a machine breaks.
Having said that, I have had physical keys lost and stolen, so there is not much difference.
Fortunately having a support agreement, they are covered (although a small fee to replace does apply, which I don't think the replacement fee is applicable with software keys - but I may be wrong about that.).
As far as I know the software licenses are stored in a company pool that is set up by Graphisoft, the distributor that the licenses were bought from.
This pool is not on a physical machine, at least not on your side.
You download the license to a particular machine, but where this license is saved i am not sure, but it is not something that can be put on a USB key.
Even on the hard drive, it might be linked to the Operating system, and motherboard/CPU in some way.
So even swapping the hard drive to another machine may not work.
However, when you start Archicad with no license, dose it give you an option to use an 'Emergency' licence?
This emergency license can be used for a period of days (not sure exactly how many), to allow you to work while you contact your distributor to organise a replacement license.
If you have no support agreement, I have no idea if there will be fees involved.
But your local support are the only ones that can replace the license as far as I know.
Definitely not a silly question and you don’t need to be sorry either.
I hope you get your issue sorted for your business.
The support company will always benefit greatly by helping out of date users like us because you encourage them very much to get back on board when they can afford it.
I have personally experienced great support with my company where I live.