While such a license might exist, it would not be an Open Source license (as per the accepted definition, of which it fails to meet roughly half the conditions), let alone Free (Libre) Software.

You are publishing source code, but that alone doesn’t make it Open Source – otherwise, the software I write for my day job (we deliver sources to most of our clients) would also qualify as Open Source.

In case you’re not too attached to the Open Source label, just look in other directions. There are probably products around that use a similar licensing model; see if their licenses fit your needs.

And of course, as always: if you want actual legal advice, consult an actual lawyer. More so if this is not just a pet project but something you rely on for your income.

What you are talking about, limiting redistribution, goes against the definitions of open source and free software. If you find such a license, it won’t be either of those.

So, I recommend you get a lawyer and you two come out with the terms of the license you are thinking about, with whatever other restriction you might want to add, and whatever freedom you might want to give to your users.

Some things to ask yourself:

• Will users have the right to create derivated works — change the code?
• Will users have the right to host their derivated works? (if those are allowed at all)
• Will it be possible to fork your project?
• What type of changes and what amount of them give the user freedom to freely redistribute your software, if any?
• What do you expect to gain by opening the source? Do you expect new contributors? Or do I just want the users to be able to see the code?
• What is free software? What is open source software?

Note: You say «I guess this would be even more restrictive than AGPL». The addicional restrictions in the AGPL are to ensure the freedom of the software. They do not limit the users in any way, just demand additional conditions to the developers. You might agree with those additional restrictions or not, but they certainly have nothing to do with the ones you want to impose.

The Elastic License is one such license:
https://www.elastic.co/fr/licensing/elastic-license

It says the following:

You may not provide the software to third parties as a hosted or managed service, where the service provides users with access to any substantial set of the features or functionality of the software.

If you are the sole copyright holder (holders) you can use any license you like. You would use an open source license to get brownie points or to help other developers, and to use their improvements to your code for free. If I can read your source code but cannot actually use it due to your license, then you don’t help me, I won’t improve your code, and you won’t get brownie points.

If your code is derived from GPL-licensed code, then you can use it freely for your own purposes (because GPL allows it) and you can publish it under the GPL and a GPL-compatible license. What you are asking for is not GPL-compatible, so you must publish your derived code under the GPL-license.