If you want to alkalise your body I think you CAN drink with meals, as long as it are alkalising drinks, such as mineral water, green tea, orange juice (the real thing, most brands have added sugars, 100% pure is a little bit more expensive) etc. I usually drink things like that with my meals. For some reason I couldn't open the link you posted, so I dont know the theory behind that.
Actually, the lemon thing I am doing works alkalizing, so maybe you can do it at the same time. Hehehe, I dont want to sound to pushy, but I found something that works, and I want other people to feel as good as I do right now (*violin playing in background*)
How are you alkalizing? Do you eat "bad foods" or also "natural" like me? I found it impossible to alkalise eating junk, I dont know why that is. At work one guy thinks I have anorexia because I never eat candy and things like that anymore. Also this afternoon I was in the supermarket buying lemons (three cases) and the cashier asked me "What the hell are you going to do with all those lemons ?!" I mumbled something like "I put it in my tea" and fled the scene (I didnt want to go in depth in the lemon science LOL as there was a huge line behind me ) Ah, the adventures of a lemonjunkie
Keep me updated with your progress.