You're spreading yourself too thin. Spending five minutes on an exercise or learning a song is probably not enough to make any headway on the exercise or song. An hour is not a lot of time, so don't divide it too much. As a rule of thumb, my minimum block of time is 20 minutes to spend on an exercise and, even then, I don't feel good about only spending 20 minutes on something.
Pebber's preferred picking technique is a combo of scalpel and Sarod. In theory, if you were able to get these techniques down, I suspect learning alternate picking wouldn't benefit you too much. I would do away with practicing alternate picking AND Sarod AND scalpel. Spend 20 minutes on Sarod picking, with 3-to-4 minutes on each string, without fretting anything (see Pebber's Daily Practice Routine Videos). Then, try to double-up on your exercises: Spend 20 minutes on chromatic exercises WITH scalpel picking. Spend the last 20 minutes on scales. As you pointed out, the trills, spiders and ladders are conducive to television zoning-out, so do those then, if you must watch television. Do this for several weeks, and do not change what you are working on. After that, perhaps switch out the 20 minutes on scales with 20 minutes on songs. Do that for several weeks, then switch back.
An hour isn't much, so there will be some compromise (e.g., not learning songs when learning scales, and vice-versa). But don't compromise on the picking exercises.