I would suggest a rather different approach. I would install fresh new 10.3.6 and using WLST scripts will reconfigure the same domain and deploy all services. You then will have two environments which you can switch over between. In case the new one does not work, you can switch back to the working one.
Instead of scripting domain configuration you could create a domain template in 10.3.5 and try to use it for the new one in 10.3.6.
In place configurations leave you with limited options to revert back to a working environment in case something goes wrong.
I agree with Anatoli with creating a fresh install on the new machine for the 10.3.6 home.
However, I would take a clone of the domain and copy that to the new machine.
Upgrading the domain is described here: https://docs.oracle.com/cd/E23943_01/web.1111/e13754/upgrading9091.htm#WLUPG178
It actually comes down in changing the scripts to point to the new middleware home. That can be done manually or using the domain upgrade assistant.