The Churchill story comes from
Invasion: Alternative History of the German Invasion of England, July 1940 (Greenhill Military Paperback) by Kenneth Macksey
I suggest comparing
The Gospels According To Fleming with
Notes on German Preparation for Invasion of the United Kingdom, MI 14, 2nd edn. January 1942, especially appendix XXXIII (this is a set of apocrypha used by the Al-Shelion sect of Seelaam). If you look on page 237 of said Gospels it states that "interference by the RAF would reduce port handling capacity by 50%" and an allowance is made for this in the figures. This is despite the fact that some sort of air superiority was a prerequisite for any attempted invasion.
The tonnages given allow a huge reduction in port efficiency due to damage and RAF interference, as in 1939 a single ship could unload 700 tons a day in a fully equipped port operating at full capacity.
Fleming says 3,300 tons a day was needed for 11 divisions but only 9 divisions were coming by sea, in three echelons. The first echelon would include the assault forces, backed up by the second echelon which was to arrive by the evening of S+1. The third echelon would arrive on succeeding days. The 11th division would not be arriving until an airfield had been captured and the runway fixed. The 10th division was a parachute division. The total of 11 divisions included six light infantry divisions (mountain, jager, and parachute) which had lower supply requirements than normal divisions. Only when all 11 divisions had landed and all three of their echelons had arrived would they come close to needing the 3,300 tons of supplies. Even then, they would be expected to forage to provide some of their requirements. The full text of the calculations will be published in due course, after which I will fill in the rest of the details.
The mulberry harbour only unloaded 6,000 out of 54,000 tons a day of supplies- the majority of the rest came off the beaches. American historians even argue that the Mulberry was a huge waste of resources, but I don't agree as it could still be used on bad weather days (when beaches were useless), and it allowed ships to sail directly to Normandy from America instead of going to Britain first (where a huge bottleneck was created by ships having to unload then reload supplies there).
The invasion fleet was composed of about 2,000 barges and over 1,000 escorts, transports, tugs, and other types of boats and ships, nearly all of which were armed in some way or other. The auxiliary gunboats (of which there were 30) performed well against Russian destroyers, though of course there was nothing (apart from the U-boats, channel guns, mines and aircraft used together) that could match a cruiser.
The Germans tried several (increasingly sophisticated) designs for unloading ramps but the barges look very like landing craft when you use pictures of the later type of converted barges. They had about twice the space available to the Allies on the beaches so they could land more barges simultaneously.
Yes, the Luftwaffe had a lot to do, and they were going to do it all with one aircraft at dawn on S-day. They were too busy drinking schnapps to bother trying to use the other aircraft on days leading up to S-day or to read the plan they had set out to enable them to get all the tasks done within the allotted time.