Honestly kids first over anything. In looking at this, I would say the best bet is see about a long distance relationship. It will take her time to get settled there. As it sounds it looks like you have a full load between 6 days a week and shuffleing around trying to see your kid as much as possibile. Considering she has allot on her plate, it doesn't sound like she will be jumping into any relationship soon out there and that leaves the whole long distance thing open for you and her. Try to take weekend visets and what not when you can. Maybe go out for a week during the holidays and what not. But let her get back on her feet, as a good friend/lover/etc you owe it to her to give her time she needs to get her life going for her and her child just be as suportive as you can. If it is ment to be, then nether of you will be looking else where. If it is not yeah it may suck who ever is on the heart broken side in the end but it is worth the risk if its truely your one and only. Custody wise on your side, if things went down the road of marriage, then you have that bonus to getting more custody of your kid. I am not saying elope and get married, but it gives you the option later on if you guys go down that route to then move other places if its in your cards to do so.
But one sugjestion, changing school the older a kid gets the harder it is on them. Being the new kid is never fun so dont rush into anything.