Warning, what I'm about to suggest is unprofessional and frowned upon but is happening more and more these days as companies are looking at software professionals as units and not people. This also assumes as a 57 you are a more junior developer which there are literally thousands of at Schwab.
Consider accepting the job and setting a start date of two weeks after labor day. I don't have insider info, but it sounds like STS will start letting people go after the labor day transition is over. You got them through the transition and now you are disposable.
If you get laid off then you can swing into a new position and have your severance.
If you don't you can tell the new role something amazing once in a life time came up and you've needed to reconsider accepting the position. You can stay here at Schwab and continue to look for other options. There will be numerous software jobs out in the market both fulltime and contract.
If you back out on the last minute, you will be burning a bridge with that company, but I guarantee its happened to them before and they will move on without thinking about it. See above most companies view you as a unit not a person. Who knows, maybe they will cough up more money or benefits. It could make you look more desirable. I have colleagues that have done this and they have been able to get other jobs easily. The market place is strong for software developers.
Good luck. Its nice to have choices.