Can I ask for a change of date?
Yes, it is possible to ask for a change of date. But it's important to remember that you signed an agreement with them about advising them immediately about changes in your circumstances. If they decide that you did not keep your end of the agreement or if they decide that your dates are no longer supported by your premise then matters will be worse.
And what would be the specific process of achieving this change?
- Prepare an explanation and take everything back to the VFS where you
originally submitted. Unlike an Immigration Officer, an ECO has no
powers to cancel existing leave unless it's his fault, so the
outcome is doubtful and could go either way.
- Submit a fresh application using priority services if the situation warrants it.
Is this worth the trouble?
No it is not, but that's strictly an opinion. Based upon what you wrote, it's a lot of extra paperwork for a very small gain against the risk that matters could be worse. You were fortunate enough to apply successfully in the USA considering that Accra has the highest refusal rate known to mankind. I suggest letting it go and enjoy your visit to the UK.