A cloud solution is indeed an option, however not a very palatable one. The main problem with a cloud solution would be pricing. From what I can see, you can get 1TB for about 10€/month. We'd need substantially more than that. The cost is feasible and not excessive, but frankly it's a bit of a joke to have to use someone else's server when we have our own.

You want to bypass system level access level restrictions with some form of control but not go through your company's standard method of doing so because of bureaucracy?

Yes. Not a company but public research, which means asking for a group change may lead to several people in the capital discussing on whether that is appropriate or not. I'd like this to be a joke, but it is not. We'd surely get access eventually if we do that, but that would lead to the unfortunate side: if we work in that way every new person who has to get in has to wait all that paperwork.