So yeah. The Allied landing craft used during D-Day were, on average, about 12 times the size of the Pilabos 39. That makes my factor of 10 pretty-much bang on doesn’t it?
No, it does not, because you made an assumption that Germany would need the same amount of troops and resources for the invasion of UK as the Allied invasion of Europe. Germany did not need a force that large nor did it need to sail over the ocean - that is why I did not assume that the landing vessels were of the same size, while you did. Also, you used the lifting power of a barge to determine how many landing crafts you would need - and that is how you got yourself the 10 factor. That is some bad math. That barge, if you only look at a lifting power, would be able to load 10 M4 Shermans or 15 Panzer III. Good luck fitting them on. If you use lifting power in order to do the calculations, let me do some real math for you.
Lifting power of the barges was between 360 and 620 tones. Average - 490. But as that is a bad number to use, we do not know how many of what type of barges were there, let us assume that all were the smallest ones with 360 tones capacity. 2400 were gathered. That gives you 860.000 tones of cargo lifted in a single run, if you use lifting capacity as variable here, as you did.
Now, let us compare it to the D-Day. Almost a month after the invasion, 850.000 men, 570.000 tons of supply. Now, men and supply alone would add up to (let us say that your average soldier is 100kg with his gear), it gives you 655.000 tones being required to be lifted over a month of a D-Day invasion.
So, if you use the lifting power to determine how many landing craft you would need, as you did and got to 40.000 and the 10 factor, it would seem that a single run of German barges would transport more in the terms of man and supply than a month's worth of transport for a D-Day. Around 25% more. Hell, let us even calculate in the vehicles, again over a month time period. With 148.000 vehicles, 10 tones average (tanks were 30, but most of the vehicles were half tracks, trucks, jeeps that were way below 30 tones, so 10 ton average is fine), you get 1.480.000 in vehicles, 570.000 in supply, 85.000 in men, to the total of 2.136.000 for a month of the D-Day. The amount barges, if you use the lifting power for the calculations, would transport in 3 runs. If we take that all of the barges are the smallest ones.
That is why you do not use the lifting power for your calculations but use the actual number of soldiers, vehicles and supplies that are needed and how much could be fitted onto transports. Otherwise you get some bad math, 10 factor and 40.000 landing craft needed.