There is a long dovetail on the front. Im not sure what sits under the rear claw. But, like you said, it would be nice to get a nice set of talley split rings on there somehow. Without drilling. I just dealt with one hole in this gun, Id hate to add more.
OP, it sounds like you have machining capabilities???
I have modified similar bases for different rifles, including one recently on a custom 98 project.
The easiest method is to purchase or make up a Picatinny style rail, with enough depth that you can machine the desired widths and depth needed to install it in the present claw mounts.
It isn't difficult, if you have the equipment or a good friend to help.
By modifying a Picatinny base to fit between the claw mounts, you will not only preserve the look and intent of the bases but preserve a very valuable and capable mount system.
I have three different similar style mounts on different rifles. One I've left original, because I've got a couple of excellent scopes with proper ribs to fit.
One I've modified by machining the bases of off the shelf rings to fit into the dovetails of the claw bases and this was very tedious, especially getting them absolutely level and square to each other. I used Burris Signature rings to take up the very slight differences of a few thoushandths of an inch.
The other has a modified Picatinny rail, which had to have two different length/depth bases cut to fit the dovetails on the claws, very similar to those on your rifle.
A blank Picatinny rail base costs around $200, for a 15cm length and IMHO would be your best overall option and still preserve the originality/purpose of those great claw mounts.