Deduplicate Clipboard Sync Notifications

I use two computers at work (yes, it's a frustrating situation due to a few different unavoidable things) that have their clipboards synced both to each other and to my phone.  As a result, whenever I copy something on my phone, I get two notifications on both computers (one from syncing the clipboard with the other computer and one from syncing it to my phone).  I know it would be possible to sync two of the devices to one device but not to each other, but because of a spotty internet connection, I'd prefer to have the redundancy in case one device can't reach the internet but the other two can.

I believe a simple solution to this would be to just check if the incoming clipboard data is identical to the current contents of the clipboard and not perform the sync if they are.  Is that possible?  Would this break functionality elsewhere that I'm not aware of?