Nothing wrong with factory rings. See no advantage in using a picatinny rail. IMO it would raise the height of the scope for a poor cheek weld especially with the factory stock.
One thing you could do is have a gunsmith lengthen the existing mag box. I had it done with all three of my M77s.
I agree that factory Ruger rings are a good strong setup and allow the lowest possible scope mounting. However, there are several advantages to going with a picatinny rail.
The reason I, personally, went with a picatinny rail (and why I recommend doing so) is to gain the flexibility to use any brand or type of picatinny rings desired. Previously, I have had to order Ruger rings when I needed them. Standard picatinny rings can be had anywhere and in whatever style desired or required, including QD rings, something not afforded by factory Ruger rings. Moreover, the Ruger rings do not offer a means to gain additional elevation in the mounts, as is often needed for long range shooting.
I have found it convenient to be able to utilize the same style of rings on all of my rifles, which makes it a simple matter to keep whatever I may need on hand, rather than have to chase down oddball parts.
As far as correct comb height is concerned, I had to use a cheek pad to properly align my eye to the scope, even with the factory rings. The only difference between the two systems was the thickness of the pad, which is not much of a downside.
As for lengthening the factory mag box, can you shed some light on who offers this service and what length they are able to achieve? I am aware of an option to purchase bottom metal that allows the use of 3.6" AICS mags, but I much prefer an internal magazine.