Is there a way to put the 2/3 section of rings on a scope in such a way that they are unlikely to scratch it? I mean rings that aren’t divided into semicircles, but more into 2/3 + 1/3, where the 2/3 section must be snapped over the scope tube. I really dislike the design, but maybe there’s a secret to the mounting process known to everyone but me.

Nope, they "snap" in over the scope tube. You can manually pull them apart to help minimize the scratch or pressure needed to get them on. But I try not to use those style of rings, unless I have to.

Get new rings.

Yeah, there are too many other affordable options.

Although I bet a piece of paper on each side will protect the scope while sliding it over.

In this particular case, changing rings isn’t possible otherwise I’d make an immediate switch. The paper trick is a great idea. I’ll give it a try.

The paper method has worked well enough for me in the past that marking up the scope tube was never an issue. It seems like the rings were Leupold QRWs, but that's info retrieved from a cluttered old memory.

These rings (Dentler), are very similar to the Leupold QRWs, which I’ve also used and also dislike for exactly the same reason.

Why can't you switch rings?

I'd never use a design like that and can't think of a good reason for anyone else to

Mounting options for a Mauser M03 are very limited these days as the factory has largely abandoned the model. Dentler makes quality bases and rings, that are available and work very well, but their rings are the type described previously.

Does anyone make a Weaver style base?

The rifles have builtins in a proprietary format. Unfortunately, like magazines, they are no longer producing the factory mounts. It is a beautifully designed rifle, but the abrupt collapse of factory support is painful.

Can't remember which, but some Rugers have scope bases as part of the top of the action. However, there is a pic rail that will attach to Ruger's base.

YouTube: Mauser mount for MO3

Excellent, but unobtanium.