Well Mark, that's unfortunate information There's not much more to say that's not already been said.
If you have savings over £16,000, you can’t usually get income based Jobseeker’s Allowance.
Yes your quite right, that for each £250 of your savings over £6,000, your benefit is reduced by £1 a week
I guess this means your JSA will be reduced by £32 per week based on being £8k over the limit.

How it came about isn't the big issue, but you'll need to get back on track with the JSA and get you finances regularised for at least one month before submitting the visa application.

The principle facts remain the same in that you must evidence a disposable income of £111.45 or above.
Savings may help you, but these in themselves cannot be relied up as under the financial requirement exemption you must have a level of regular maintenance income at or above income support levels.

You case is highly marginal. As I've mentioned before you need to seek the guidance of your immigration advisor. But your ability to demonstrate maintenance sufficiency is marginal and fragile.

On top of that, it's likely that your JSA overpayment may need to be repaid.

I'm sorry I can't offer an instant solution. It still quite surprising that your JSA claim was able to be processed in error unless you initially provided inaccurate information.