I think, but would like someone like Thomas Thumb, Credit Guy In Dixie, Brutual or a moderator to confirm if possible.
I believe in Texas, your statue of limitations is 4 years on consumer debts ( if you have not made a payment at all in the past 48 months, which restarts the date). However, for it remaining on your credit files, will be for a full 7 years. So they can not sue you now, also long as you judgment was ever placed against you.
Have you pulled your free annual credit report that shows when all the accounts are due to age off? If not, due so.
You spoke of obtaining a mortgage, how soon? less than a year or 2-3 years down the road?
I think obtaining 2 minimum credit cards more will help you. Once these accounts age off, all you have is the Chase. 1 card.
You optimal want a bank card, stay away from store/retail cards if at all possible. Keep the Chase in good standing.
Once you burn a big bank, Discover, etc, it is hard to get back in their good graces. However, down the road a few years with a rebuild, Citi, Amex or other additional Chase cards are feasible.
You may have to start with an Open Sky secured, think they are soft pulls, so no inquiry. They are starter cards, but one of the better than some of the other ones. If you have a good bank or especially a credit union relationship, that would be even better to obtain their card.
You need a loan somewhere, sometime for the credit mix percent scoring. (30-35 pts). Here on the forums, there is a thread about Shared Secured Loan. The thread is for purposes of obtaining a small loan, but at a long term, 48-60 months. Yes, there are lenders you will see that will do it on those terms. You obtain it, however with a lender that will accept a large payment that catapults your due date way in the future (that is the KEY). Because you pay it down after opening it to less than <8.9% of what your borrowed. This is the threshold of utilization that gives you the biggest point gain. So you gain points for having an installment (bank, not finance company), plus the low utilization. Please use the "Search all content" at top of page, but to the left, drop down menu to all boards. You will see the Shared Secured thread (many pages) and learn there.
The only other advice, and I would be 100% positive they would is try for a pay for delete at a reduced rate. They know you are past being able to collect if in fact Texas is 4 years for the 2014 chargeoffs. So they would take a settlement only if in return they verbal or preferably agree to delete the lines across all bureaus. You won't see the biggest jump with one or two, but this is the most damaging to mortgage scores than the other FICO scores. Once the last one is deleted or ages off, your scores will gain huge points!
