I don't think a cab to/from HND will cost $100 each way, even given that Tokyo cab fares are 20% higher between 11pm and 5am. More like $70, and there is no tipping. The MO would be cheaper to get to than the Shang.

The issue on late night and early morning transport for HND has been discussed extensively in the FT Japan forum, you should check there. The trains should still be running for your arrival if you keep moving through the system, but not for your departure. There are some late night/early morning airport busses at a premium charge (but still cheaper than a taxi for 2 people).

Any Tokyo luxury hotel experience will be outstanding. There are threads in this forum comparing the various Tokyo luxury hotels. Do a search, maybe you can get it to work for you (I rarely can get search on FT to work for me!).