I got back yesterday. I decided on the Holiday Inn Express at T4 because it was not worth paying for a 4 or 5 star hotel for an 8 pm to 6 am stay. I found the HI Ex easy to get to, and cost me only $101 for the night, including the buffet breakfast. I took the free bus from T5 to T4 (a nine minutes ride) followed by the enclosed walkway from T4 to HIEx (a 5 minute walk). On the way back I took the walkway to T4 and rode the free train to T3..
The room and bathroom were small but the bed was very comfortable, and the buffet breakfast really helped, given my tight schedule. The hotel is new and it felt good.
I had dinner at the adjoining Crowne Plaza (same building) which had a nicer restaurant. Overall I was happy with my decision. My only gripe was that the HI Ex is listed as a 3.5 hotel. In reality it is at the most a 3.0 hotel, but it was a very comfortable hotel that was easy to get to (no transportation cost) and it was perfect for my situation.
Now I feel more comfortable about LHR. I found many helpful people who worked there and gave me directions. There is plenty of free transportation available, the immigration was done electronically (meaning faster), and going through security was easy. I was happy that I didn’t have to take off my shoes.