Receptionist phones

You say you moved from a cloud system to an On Premise Skype for Business server?  Or to the Cloud Skype PBX, since you say there is no auto attendant, expect preview?  Think that is what you mean.  So you actually moved from one cloud system to another?

Yes, there are solutions out there like (sorry if no links are allowed) landiscomputer.com / attendantpro/

Not sure if they still support that product looking at support article dates, almost 2yrs old.

http://www.enghouseinteractive.com/

I usually just have a regular phone similar to staff as a backup in case the soft console app isn't working.  Audio path is the computer with a bluetooth or USB/wireless headset.

Is this what you are asking?  Think you would need to have bluetooth on the computer to pair it and get voice through that channel, only use the phone as a backup.