My concern is adequate clearance over the chainstay at the rear with the small cog. Does the chainstay protector cover the inside and top of the chainstay where the chain runs over? A single incident with the chain running on the carbon stay could ruin the chainstay. And dropping or slapping the chain on a carbon tube could cut or crack it.

From your photo, it looks like there is very little clearance over the chainstay when in the small cog. If the bike were mine, I would not run that small cog. Even if you don't run the small/small on purpose, one accidental bad shift could cause permanent damage. I'not not sure that shortening the chain would do anything to reduce the risk. Some frames just aren't designed to work with some gears.

At the very least, I'd recommend that you install the 12T small cog from your old cassette onto the new cassette. That would allow you to run the a longer chain and improve the clearance over the chainstay when in the small cog. I doubt if the old 12T cog is worn significantly, even if other cogs were used up. Most people spend very little time on the small cog.

I recently picked up a used 13-23 8-speed cassette from another BF Member so I could assemble a 13-28 (using a new 11-28 cassette for the rest of the cogs) cassette for one of my bikes. The bottom cogs showed considerable finish wear, and I could see exactly wear the previous owner spent his peddling time. The two smallest cogs (13T and 14T) showed barely any use, and were perfect for my purposes.

I'm no expert sizing chains, but I read that a four link overlap was supposed to be correct. Rear derailleur looks pretty stretched out, and the chain looks like it's bordering on too short when in the big-big. I probably would not have shortened it myself. If the rear derailleur does not have the capacity to tension/wrap the longer chain, get a medium or long cage derailleur.