Turning your schedule around is very bad for your ADHD symptoms. I do the same thing, and I can tell you that I was far more successful with managing my symptoms when I was on a steady schedule.
That said, in your post you discuss a problem with consistency in taking your medication. What sorts of issues does this inconsistent dosing cause for you? If you're just concerned that you're taking your doses at inconsistent times, I wouldn't worry about it. Take your dosage at whatever time is "morning" for you, and as long as you're not having any problems, don't lose any sleep over it (pardon the pun
If, however, you're having sleep issues or symptom issues, the problem may be more fatigue than medication. Turning your schedule around is not a natural thing, and will have consequences for anyone, ADHD or not (I'm not necessarily advocating that you don't turn your schedule around, just suggesting that a med change may not help).
As for a non-stimulant med, there are more now than ever to choose from: I have benefitted significantly from Wellbutrin; Bob (ADDprogrammer) has had luck with Intuniv; and I finally saw someone have symptom improvements on Strattera (I was shocked, but it seems to work with some people). Each works differently, so you may have to try each before you know which is right for you.
Best of luck.