Incorrect dates on visitor visa

[sparcher]

I'm planning to be in the UK from December 15-June 14 as a visitor. I received my visa in the mail, but it has the wrong dates on it: December 17-June 17. After two weeks of querying the immigration office about what I should do, they finally got back to me today and gave a fairly noncommittal answer, saying that I could get the dates changed, but that it would take up to 20 working days from the time that they escalate the issue, and referring me to the gov.uk information stating that U.S. visitors don't need a visa, then stating that the onus is on me to make a decision.

I'm wondering if anyone here has experienced a similar situation, or has any insight as to whether I'll have trouble passing through customs with my current visa. I can't get the dates changed on the visa at this point because they may not return my passport in time for my trip. I could change my flight to arrive on December 17, but this will cost me $600-$700 and upset a lot of plans that I currently have. Or, since I'm allowed to enter the country without a visa as a U.S. citizen, I could go for my currently scheduled flight on the 15th with printouts of my itinerary, showing that I plan to leave within the 6-month timeframe on June 14, and of my email correspondence with the immigration office regarding the issue, and hope that these will allow me to pass through customs. Any advice would be tremendously appreciated!