I think all the replacement ones are that large as I have the same one. I assume everything on the replacement should fit into the case with exception of the IEC cable. Besides, you shouldn't hang out with anyone that doesn't have a bunch of spare IEC cables anyway.

I have a few Rio's but I never looked at the power brick that came with them. Both of yours say 12 Volt DC. My Empeg MkII came with a 15 Volt adapter, and I use a spare 13 Volt which works also. However, the last time I used a 12 Volt on my MkII, the VFD would go blank when the hard disk spun up. Maybe this issue was fixed on RioCar?