You know what I would do, I would have a hearing and get everything spelled out on everything as being causally related, and then I would negotiate, that way you can negotiate from strength, especially if you can be classified, then you are guaranteed the $400.00 weekly benefit if found PPD. Your right about how they want to low ball you. Think about it, and this is no dis respect to anyone, but if you are hurt and been off of work, the bills have piled up and the cash flow is running out and you see an offer like this pop up and you think WOW that would be really great to take and get everything taken care of financially BUT, then you realize that you are still hurt, in need of medical care and go and get a prescription filled or see a doctor and find out how much things really cost (remember, you wont be paying as the insurance company did at the comp rate but the doctors rate, cash or check please no IC) and you realize that that $$ they offered wasn't sh*T! Why does your attorney want you take this offer; could it be the 10-15% off the top for his/her services, and knowing that you will be out of the system? Hum, if my attorney knew what you are going through and that you have a winnable case then he shouldn't even suggest a settlement without what you request, seems reasonable to me if you feel the B & F can be settled without future medical vs. no $ and keeping the asthma's medical open.
Is special funds involved, if not then you definitely should stay the course you have plotted!