UPDATE: arrived in LHR today on time at 11am. Quickly made it through immigration and customs and easily found the arrivals lounge in terminal 3. Showers were clean, well stocked and nice. They even have a valet service that will iron your clothes while you shower! The only drawback was the ventilation, or lack there of, easily turning your shower room into a steam sauna. The lounge was not crowded and had a nice menu. Thanks again for all the help!