A decent idea though, I will encourage you to get in touch with your target schools as well. Ask what universities/colleges you can do those courses from. I mean, think about it: The legitimacy of that course will also depend on the institution offering those.
Moreover, it is your time to get a 51 in Quant on the GMAT Exam. I have worked with many Non-engineers who had a 50-51 in maths, and we always liked creating stories that projected that as a strength. That also assures a school of your ability to perform in crazy quant driven curriculum. Scoring a 46 on quant, and throwing an alternate transcript may not be the best idea. And remember: Getting a 51 on Quant isn't as difficult as it may sound.
Once again, do get in touch with the admissions committee members. Not everyone will respond to you, but even if you start with the colleges that are not on your priority list, they are very likely to give the same responses as your preferred ones.
Good luck to you !