When you have health issues and need the money you will do what you can do with what you've got. I feel your situation big time.
If that one big picture in post # 26 is representative, I say yes you can do it. Far from ideal but you could.
1) If all else fails, walk the land to make sure what objects and debris are there, mark anything TOO bad, and then just go after it slow with the MMM set high. Don't let it bog down and burn belts or do damage. If that happens you lose.
2) Talk to your customer and see what his real expectations are. How short does he want it mowed? How flexible is he? Not good idea to start if you aren't going to satisfy him. By the hour versus price to do the job offer pros and cons.
3) For sure the brush hog is the right tool. Since you can borrow a brush hog, make sure it is 5ft or less. You can run a 5ft hog with your BX in that kind of weeds without too much grief. There are several issues for you with using a hog. First your lift arms may not want to spread wide enough to mount the hog. Cat I vs Cat II ? Second, the driveshaft may be too long and might have to be cut shorter to allow you to hitch (I doubt it.). I assume you have to pull the backhoe or is it off ? Do you have lift arms or have to add them to the BX? If you do not already have lift arms for your BX that almost rules out using the hog for a single job...the arms and lift links kit etc are NOT cheap.
I'm going backwards in this discussion but FIRST, before you even think about other options, check the compatibility of that bush hog. If it can be made to work , do it.
Only if you can't use the hog, go into it slowly with the MMM.
If able to use hog, get someone to help you pull the MMM off before doing the cutting.
[There are so many unknowns here -- what you have and don't have to work with, what help you have, how bad your physical limitations are, etc. Good luck!]