I would love to see the results of the first idea you've posted, it's always been something I'm curious about.
I'm currently on a somewhat keto diet ( Just had my refeed during the game tonight ) and I prefer HIIT cardio to LISS cardio, but I'm doing LISS simply because I'm under the impression that HIIT cardio will cause me to use carbs which means my protein would be converted as I don't have any in my system.
A possible solution to maintaining a low carb diet and gluconeogensis (conversiton of protein to glycogen) is to consume Medium Chain Triglycerides, MCTs.
As you're probably aware, MCT are "carb like" in their digestion time and can be used for energy production.
Here's an article on them. http://www.answers.com/topic/medium-chain-triglycerides