If I were you, I would hold fire on buying a USB-eLicenser and wait to hear back from support. You should be in the situation where you can run Dorico 3.5 on your laptop and Dorico 3.1 on your desktop, since having reactivated on your laptop, that doesn’t deactivate the license on your old computer, but only one Soft-eLicenser can be the current one and the one that MySteinberg expects you to be updating. If you need a time-limited license to run Dorico 3.5 on your desktop, then please send me a private message and I’ll send you one.
Please do note that although you can use the ‘Reactivation’ workflow to move your valid Soft-eLicenser from one computer to another, and that this does not deactivate or remove the licenses from your old computer, with the current licensing scheme, only one Soft-eLicenser is considered to contain your current license, and the update activation code you have purchased is a single-user activation code that will only update a single installed Dorico 3 license.
I’m no fan of this licensing system, as my dozens of posts on the topic over the years have made clear, but unfortunately this is the system we have at the moment. Work is underway on a new licensing system, and hopefully we will be able to move to that in a future version, which will eliminate these difficulties and make it both officially supported and trivially easy to run a single license on two computers.