Jova
Part of the reason why your flushes may not be getting the yield you want is because you're pushing it back two hours. The 10pm time is deliberate--it gives the potion an hour to act on your gallbladder and cause it to contract, sending the stones down the part of the ducts that open up and empty into your bowels. From 11-1 and 1-3, your gallbladder and liver dump their toxins (and the stones) into your bowels. If you drink your potion at midnight, you give yourself hardly any time for your gallbladder to dump its toxins into your bowels. Also, while I can't verify this, it seems that when you're gallbladder is contracting violently (when you throw down the potion), it'll be difficult for it to dump much of anything into your bowels. If you take the potion at 10pm, your gallbladder will have a sufficient amount of time to settle down to resume its normal business.
Don't be too concerned about not being able to sleep at 10pm. I've found that whether I'm asleep or not makes little to no difference on what comes out. If you're adamant about sleeping at that time though, go to bed at 9 or 10 for a couple nights beforehand with valerian root, and wake up early so you're tired by the appropriate time.