Branding? Seriously? Do you not hear what the rest of us are saying? Rice IS the brand you want to be associated with. Just check the employment stats and % in industry at any of the schools you're looking at. If less than 2% of the graduates go into your target industry, you can guess than 98% won't have any interest in you.
I wouldn't delay applying at all. Neither would I bother with H/W/S. Apply to one that's truly your dream, but it's a much better use of your efforts to focus elsewhere. Go to a school with a history and reputation for Energy, you will get courted far more there than at H/W/S. Yes, Shell/Chevron/Exxon go to top tier schools. But the smaller and mid-sized Energy companies won't. I'd think it's
better to go to a school where you have many companies interested in you and you're also interested in them, instead of going to a school where the majority of recruiters don't fit with your goals.
Additionally, in Oil&Gas especially, industry loyalty and experience is extremely important, and (at least from all the oil people I know), degrees from elitist schools are not. For example, degrees from top-schools are less common on executive boards in Energy, than in other industries.
Rice and McCombs are both good (Texas) because they have a close relationship with Energy. If you're open to it, consider reputable programs in Oil/Gas bases of Britain, Canada, or Australia (Alberta, Calgary, etc????). People have launched great careers in Energy through these schools too. You will also have a chance at more $$$ for school at well-respected program than a top-tier. The $150k sticker price isn't necessarily true, make a decision after you see your aid package. Echoing what other people said, yes, saving does not justify the lost time (especially at your age).
Your experience/profile looks similar to what I've seen recruited at general management rotational MBA programs at the supermajors. 10+ years is a bit much, but not uncommon. From what I know Chevron likes them younger from more prestigious schools (top 15 preferred, top 30 ok), and Shell prefers older, more experienced (more common to see 10 years experience). Look into general management MBA rotation programs at your target companies, all the supermajors have one. Then compare it to people on linkedin to see common traits in their work history and school. There are few H/W/S people, though plenty from Darden, Stern, McCombs, Rice...
As for the poster talking about being at the mercy of the global economy, that's BS. Energy follows it's own booms and busts... For example, heavy layoffs and downsizing in the 80s/90s, but now the industry is booming and hurting for talent. Most people in energy are under 30 or over 50, so it's a great time to get in and have the ability for rapid advancement.
If H/W/S is your dream, fine. Just saying, if oil and gas is where you want to go, you don't really need it. You're far better served getting GOOD into a program ASAP, than wasting time for a desperate shot at ultra-super-elite program later. Good luck.