Highest introductory cashback
 

I have about $5000 of hospital bills I need to pay and will probably incur a few thousand early next year as well. I've tried negotiating but none will budge and I've delayed to the point that it will goto collections soon.

Therefore, I'm planning to pay the bills off. I'd like to sign up for the highest cash back rewards card I can get and put it all on the credit card to get some amount of savings.
(I have enough in my bank account to pay it off so that's not an issue and my credit is in the 800's)

The best card I've found thus far is the "HSBC Cash Rewards Mastercard" which gives 3% on the first 10K for the first year + 10% so really 3.3%

Before I apply or this, I want to make sure there isnt a card I missed.

depends whether you want to keep the card, or use it for additional purchases outside of the $5k bill

HSBC:
5000 * 3.3% = $165

or Boa Cash rewards
$200 bonus after spending $1k (you'll need to spend $6k on HSBC to beat this)

or CapitalOne Savor Rewards
$300 bonus after spending $3k. $0 fee first year, $95 after

BofA Premium Rewards

$500 after $3k spend, 1.5% back on everything with a $95 fee = $480 and $100 in airline incidentals.