I've just had a very good laugh when I scrolled down here and under the field where I enter my post the forum suggested a similar thread. The title reads " Restoring a sporterized P13...". I couldn't remember that thread, so I clicked - and guess what, it is your particular rifle here, but in 2013. And back then it had a scope sitting in these "rings" on top of the receiver. See yourself here: https://www.milsurps.com/showthread.php?t=46367
Secondly, I once did a picture comparison of the P.13 and a P.14 rifle. You can find these pictures in the Knowledge Libraryin the entry for the P.13 rifle, or directly here: Pattern 1913 "Trials" Rifle . If you need any additional images or better closeups, let me know.
Finally, I think the toughest part will be replacing the barrel with one in the original caliber, plus the rear sight will be an impossible task since "conversion" of a normal P.14 won't do it. Maybe you should consider leaving the rifle in .303 caliber, use a normal P.14 sight and just shorten it enough to be of fitting length to the receiver bridge. For what I know there were trials done of the P.13 converted to .303 Britishcaliber, so you wouldn't be too much off with that. Also note the "ears" of the P.13 and the P.14 rifle are of different shape. Maybe you would do better by not cutting off the "ears" of the P.14 receiver, but rather get new parts of correct thickness and shape laser cut and then weld them to the receiver.