Engineer,
Personally I think radon is overblown and so often used by realtors to reneg on contracts and put the squeeze on sellers. (ask me how I know!)
So not exactly sure I follow your situation but my concern would not be the money, but if changing the asking price/cash at closing would require any sort of re-work by the lender. This would push the deal back and be a pain for everyone. So I would most definitely talk to the title agency, they are the ones who are doing the heavy lifting and would know if you are crediting them too much back, etc. I don't think credit versus reducing the selling prices makes much difference, unless it requires new paperwork.
$1,200 for the system feels fair, bump it it to $2,000-2,500 and I bet they would take the deal.
To comment on Ketchup, the realtors commission on a few thousand dollars I don't think makes much different in the deal. If the deal was good enough for the realtor at price X, it will be good enough at price X-5,000.