A better choice for the KM might be the Do-26. It used four JU-205 diesel engines in two push-pull configuration. In 1939 279 of these engines were mounted on two different flying boats. IF combined they should allow for 70 x DO-26 seaplanes to be built followed by 86 x Do-26 float planes in 1940 [344 diesel engines] and 71 in 1941 [285 engines]; plus 56 in 1942 [222 engines].
https://en.wikipedia.org/wiki/Dornier_Do_26
These remarkable float planes could manage 208mph top speed and still cruise for 4400-5500miles @ 180 to 190mph [24 to 29 hours]. Scouting for convoys each patrol plane could sweep at least 21nm x 180 mph -each hour; amounting to about 100,000 nm^2 swept. As a rule every 26 planes built per year should enable one daily sortie. Thus this force should be able to sweep about 300,000nm^2 daily out to Iceland/Greenland and back. Enough to cover the GIUK gap daily from 1939 to 1942 .
The rest of those engines were the BMW-132/323 , and the CONDOR FW-200 is the obvious choice. 315 CONDORS could be made instead of all the Arado-196; the HE-115 and the DO-24. With top speed of 225mph and 14 hours @ 180mph, these can sweep 180 mph x 21 x 14= 52920 nm^2 per condor
1939 = 75 condor 300 BMW engines
1940 = 65 condor 260 BMW engines
1941 = 27 condor 108 BMW engines
1942 = 61 condor 245 BMW engines
1943 = 87 condor 347 BMW engines
In addition to the above 286 CONDORS were also HISTORICALLY built for LW- the combined fleet should look like.
1939 = 1+ 75 = 76 condor or roughly 154,700 nm^2 per day swept [254,000= 409,700]
1940 = 38 + 65 = 103 condor or roughly 209,600 nm^2 per day swept [312,000= 521,600]
1941 = 58+ 27 = 85 condor or roughly 173,000 nm^2 per day swept [257,645 = 430,600]
1942 = 84 + 61 = 145 condor or roughly 295,100 nm^2 per day swept [203,213= 498,300]
1943 = 76 + 87 = 163 condor or roughly 345,000 nm^2 per day swept
Combined with the Do-26 patrols this should average ALMOST 1/2 million nm^2 for the first half of the war.
North Sea is 195,000nm^2
Norwegian Sea is 470,000nm^2 [half way to Greenland]
English Channel is 25,670nm^2
GIUK GAP is 100-200,000nm^2
choices choices.