Battling Huge Rate Hike

I've got several business credit cards with high balances as I've gotten clobbered during the economic downturn. I recently found out one of the cards the promotion rate ran out and they jacked the rate up to 24%. All my other cards are 8-13%. I have decent credit (high 600's to low 700's). From what I understand even though these cards are in my business name (a partnership) they go on my personal credit.

I contacted the bank and told them my decreased business revenue is not going to allow me to keep paying the minimum payment on all my cards and that I wills simply allocated funds to the cards starting with the lowest interest rate. They said they couldn't lower my rate and transferred me to the Hardship department (this is Chase bank.) The Hardship department was going to offer lowering my minimum payment but not the interest rate. I told them that is pointless as it is just going to stretch the debt out and make the 24% interest even that much more costly. When all the other cards have 8-13% I am completely baffled why Chase won't compete (except for the fact they may be getting lots of defaults so they are attempting to collect as much as possible in anticipation of a default.)

I've done my homework somewhat and think I know how 'the game' is played. It sounds like it goes like this. Stop paying you credit card for a while (not sure how many months) - yes it will adversely effect your credit but from what I understand the bank won't negotiate with you until you essentially proven you are serious about no longer paying them. Once you have done that, you can essentially negotiate a pay-off to close the account and settle the debt. I've heard it is common to get a deal for $0.50 on the dollar or about half the balance. This seems to make sense seeing it is an unsecured debt so they can't take any of your assets and they've already collected in many cases probably a handsome profit on the interest so they are essentially just giving the interest profit back, and then some, to avoid a large loss.

What really pisses me off is that I tried to be both responsible and reasonable to negotiate a lower interest rate (much lower) so I can keep paying the card off. In my opinion they are acting very stupid in the sense would they not prefer to get the full debt paid with little or no interest versus only being able to recoup part of the balance or possibly none at all?

Bottom line is 24% is unacceptable. I will pay all my other cards and stop paying this one and take the credit hit if I have to. There's no way I will pay 24% on anything. This is loan sharking practically and should be illegal.

So my question is what is the best strategy going forward, assuming I have to stop making payments to get any negotiating leverage? How many months do you have to stop making payments before they are 'ready to deal' as I know each past month due is a negative strike on my credit report so obviously I want to settle the debt as soon as possible.

I know some of the obvious advice here is if you can pay off half the debt, why not pay off half now and try to transfer the remaining balance to other cards? Well 1) I don't have the funds to pay off half the debt, so I'll have to either work out a payment plan or do something drastic like sell a car, and 2) all my other cards are not offering balance transfers. This is typical of most banks as all the offers in the mail have stopped since the meltdown and the banks had to decrease their leverage.

Any advice is greatly appreciated.