Staying at BC will be a long walk to the front of EP for rides but if you are doing the front of the park in the morning, it's not the hottest part of the day. When our family went to EP when the kids were younger, it was hard to go from the IG to the front of EP in the morning. However, that was before Frozen and Remy. We would usually end up in the WS at lunchtime. And let me tell you, between noon-5pm, WS is hotter than the sun!! To be able to walk from WS through the IG to your room at BC will be AWESOME! You can then rest in the room, go swimming, and freshen up before hitting another park for the evening.
If the budget is too tight, I would NOT recommend CBR. As a pp mentioned, daily afternoon thunderstorms are likely and lightening shuts down the skyliner. At this point, Disney has not figured out a reliable plan for busing guests from EP to the skyliner resorts. It's chaos.
Maybe you can eat more QS meals--which is better in the heat anyways--and skip the TS meals to save some on the budget.