You pretty much describe what I do except that I do use a 1/4 of a Super Cedar. The frugal side of me ordered them in the 100ct volume for the lowest price and I pestered Thomas for a further discount. 400 easy fire starts is good value for the money IMHO. If it were easy to use a full one and forgo kin'lin altogether, I'd be in there like a dirty shirt.Regular axe like everyone should have. Just hold onto the handle way up by the bit and use it like a really heavy hatchet to split kindling. As my wood quality has gone up, my kindling size also has gone up. I only use four pieces now instead of 9 and then straight to full sized splits. No super cedars either, they work great but I'm just too cheap.
A regular axe generally has a fairly blunt angle to it and as such better suited to being swung. Specialty carving axes and hatchets tend to have a thinner edge of the wedge and are easier to "set" and control.
My problem is worsening with age. There was a time I could hit the same spot dead on with my swing. Now I'm lucky to hit the round. Someone watching me made the comment "Wow, you're like lightning". "That fast and powerful eh?" I asked with pride. "No" he said, "never hits the same place twice".