That's just the thing... they don't have a manager there at 11p... at least one that can do anything. I've encountered that before, several years ago.
But...did you seek one out this time? Several years ago, there may have been extenuating circumstances that caused the manager to be out of the store. Or...company policy on this matter may have changed.
I would appreciate something more than being ignored for a couple of weeks. Homophobic slurs aren't a garden variety complaint, at least to my knowledge. I would assume that if something like that came across my desk, I'd make darn sure to nip it in the bud and make sure the person with the complaint knew that it wasn't company policy to allow that kind of language on the floor.
How do you know it wasn't nipped in the bud? What your letter pretty much described was discriminatory behavior. I am sure the corporate office took your complaint seriously. However, put yourself in their shoes. Do they take your letter at face value or do they take a few days to investigate the situation before replying? You know you're an honest person and wouldn't make up something like this, but the corporate offices of a large company don't know this.
Maybe a demotion to the stock room would be more appropriate for her choice of language... I don't want to see anyone lose their job, especially now - but the last thing I would want to do as an employee is piss off the people who were purchasing things from the store that provides my paycheck...
Not your decision to make. Also, not your business how it was handled internally. Personnel matters are protected by federal law. Hence, the blanket statement that the matter had been resolved. They can't tell you how it was resolved, just that it was.
So I should sit back and allow the company to let someone with a foul mouth still be on the floor?

Just letting it go is a green light for some people.
Again, this is not your decision to make. It is the company's decision. If the company doesn't care enough, then that's their decision. Not yours. If you want to make decisions regarding corporate policy as it pertains to employee behavior, get a job in the Human Resources department at corporate.
FWIW, depending on the age of the employee, the term "gay" used as the cashier used it, is not meant to be a derogatory remark against homosexuals, nor were they calling you or your husband a homosexual. It's used to describe someone as just being weird or uncool (not that the employee of a store should be calling a customer weird or uncool, just that there is more than one negative meaning).
I want reassurance that this type of actions are not tolerated there. There is no reason for someone to be like that to another person.
You've gotten all the reassurance you're going to get. Unless you can find others who have been treated this way and can prove that this behavior is condoned by the company...
We are. We've not shopped there since (and that's big deal considering that is where we would go for everything other than groceries). Told several others too - but that still doesn't fix the matter.
This is all you can do. To be honest, you don't know whether or not the matter has been fixed. Even if it has not, it's not your job to make sure it's been fixed.
Complacency only allows this type of improper behavior to continue.
WOW! You are wasting way too much time and energy on this. I understand you were highly offended, but honestly...let. it. go.