You're in a tight spot. For night sports you really need at least a 2.8 to lose some of the grain. For baseball a 400mm is a a great range. I guess it will depend how much night baseball you plan on shooting. If I was only going to shoot a few night games (and did not have to shoot the night games), I'd probably sacrifice those games for the longer reach of the 100-400mm. If the majority of the games, or if you had to shoot, the night games then I'd sacrifice the reach. But with that said you really can't go wrong with a 70-200 f/2.8 as you can use that lens for about everything. I'll use the 70-200 for every sporting even I shoot, the only variable will be what lens I use on my other bodies.
I quickly looked at your website, and it appears you do some portrait work outside. The 70-200 is a great lens for that as well, where as the 100-400 not so much. That would be another + for getting the 70-200. I have no ideal what your wallet is like...but I've learned it's cheaper to buy once and cry once. Sure the sigma or early L's will get you what you need, but for the most part you get what you pay for. I've had the original Canon 70-200, the current Sigma 70-200, but now have the new 70-200 L. I could have saved several hundred dollars buy just getting the 70-200 II. It takes a 1.4 ET a lot better then the original giving you close to a 300mm f/4 for you day games. In my opinion you'll use too much IQ putting a 1.4 ET on the original 70-200. It will be up to you if spending the extra $1,000 is worth that (buying new).