Hello @donalmc,
I hope you're well.
I don't know anything about "Project for the Web" unfortunately, but if you're right that it only installs in the Default environment, then you're stuck between a rock and a hard place unfortunately.
The below won't help in this case, but might in the future, so just to add to this, the Default environment is accessed by every user in the company. Imagine you have 1,000 users, and many of them created/edited some apps or flows on a specific day. Then you rolled back to an earlier backup, all their changes would be lost. This is different to, say, doing it in a Development environment, where restoring a previous backup if often done and has little impact. I would say that might be a reason why you can't perform this task in the Default environment.
Here's a brief link about the default environment.
As @pagonza said, you should use sandbox environments such as Development environments to try out new things so that you can roll back easily. Although, of course, in this case you can't. Sorry.
Here's a link about managing environments.
Here's a link about the Application Lifecycle Management (ALM) process, which shows the best way to set your environments up and release changes up stream all the way to your production environment.
Hope this helps and good luck with it all.
Garry
