The other two commenters are suggesting something called AZEO, which stands for All Zero Except One. It refers to credit card balances. The remaining card reports a small positive balance, like $15 say.
You should implement AZEO as swiftly as possible, and that will give you a baseline of how high you can raise it without getting the derogs eliminated.
I am very surprised to hear that Cap One closed your card with only a 30-day late. Are you certain that the account (as it reads on the report) only says 30 days late? If so, I wonder whether Cap One got spooked by all your other collections and decided to protect itself earlier than later.
The 30-day late is having a small impact on your score compared to the charge-off and collections.
As IMD and BBS suggested, you should immediately begin attempting to negotiate Pay For Deletes on all your bad debts. Work with the people in the Rebuilding forum on how to conduct those negotiations. Be willing to try repeatedly with multiple reps over at least a few months before you give in and simply pay -- you have leverage now (they want your money) which you will lack once you have paid.
After the bad debts are paid (and we hope deleted) you can work on the Day 30 late (Goodwill letter). The Goodwill attempts for the Day 30 will be more persuasive if you wait until your report looks much cleaner. The general thrust of a GW letter is "Please help me out, this was a one time accident." That's a hard sell when your report is riddled with unpaid chargeoffs and collections.
When your report is far cleaner you can and should purchase the complete package of all FICO scores, which will include your mortgage scores. There's no point in doing that, however, until you have made a great deal of progress on the reports. Use free or ultra-low-cost tools for looking at your reports and FICO 8 scores while you are rebuilding.
