Might I suggest the wrong type of ships are being counted.
Take a quick look at Operation Iceberg. Long-range amphibious assault with most of the assault force mounting out in Leyte and the Solomon Islands.
7th Infantry Division assault shipping: 20 x LST, 12 x LSM, 12x APA, 5 x AKA and 1 x LSD. That is 48 amphibious ships to carry one division and attached tank battalion and an extra engineer battalion. An armored division would require more LSTs.
The Assault was conducted with 7 divisions afloat (4 x Army, 3 x USMC), two sets of Corps troops (III AC and XXIV Corps) and other CS and CSS. Roughly 183,000 troops and 312,000 tons of vehicles and supply in the initial assault and 1st support echelon.
The assault force and 1st support echelon took
458 amphibious ships to transport and land. Amphibious ships do not get replaced by "merchants". Those carry the logistics on additional runs, which must start as soon as the landing force is all ashore.
Reference for assault shipping and logistic support:
https://history.army.mil/books/wwii/okinawa/appC.htm#t4
On top of this is US 5th Fleet, British Pacific Fleet, their auxiliaries, escorts, battleships and cruisers. Then add the gunfire support ships, escort carriers and destroyers supporting TF 51. IIRC nearly 1,000 ships total.
For Okinawa, the logistics force was landing ~160,000-200,000 tons of supply every two weeks. Given the distances involved, that is a large number of ships. With typical "period" transport ships you are looking at 3-4 transport loads per division equivalent per 7-10 days.
In 1944, the average US-UK turnaround time was 77 days (43 days in port) for a cargo ship. Turnaround time includes loading, assembly into convoys, outgoing transit, unloading and return transit. This figure includes waiting for a slip to unload and waiting for the convoy to assemble. That is US and British ports without using slave labor. Ports were very congested. US to the Mediterranean was 116 days, Persian Gulf via Good Hope was 206 days. There is a 17-day transit time in convoy at period-ship speeds, meaning that each division consumes 20-24 ships at sea; add another 8 ships loading and unloading. Add another division equivalent for Corp troops and engineers (at least). Even assuming friendly, efficient labor the Iceberg-sized assault force consumes 224-256 cargo ships to manage the logistics.
That is if they can load and unload in one week on each end (which was better than the WAllies did)! Don't forget that operations on Okinawa would consume a lot less motor fuel than mounting an attack against the lower 48.
Where does that fuel come from? Persian Gulf I would assume, which increases the average turnaround time to 126 days (via the Mediterranean and Red Sea). Perhaps they create a large fuel port in Morocco, but one is still looking at trans-Atlantic turnaround times (plus the back end ships to move fuel and supplies to the African ports.
How many Corps and Divisions are needed to win? 75? 100? 150?
How many Corps/Divisions are needed in the first 60 days (because that is roughly what it will take to turnaround the initial amphibious ships)?
For the sake of argument, let's say the initial landing is 18 Divisions (6 x Corps, 2 x Field Armies). Roughly speaking 1,200 amphibious ships and 1,300 - 1,500 cargo ships for logistic support. How far does 18 Divisions get you?
The USN had roughly 2,500 amphibious ships in August 1945. It would have taken half of all the USN amphibious shipping available in 1945 to mount Operation Coronet (15 Divisions). In 1945 the USN had more amphibious shipping than has been afloat at any other time in history (by a very large margin). CONUS is a much bigger nut to crack than Honshu.
The US pre-war shipbuilding program gets the USN to 1,782 ships in December 1942 and 3,699 ships in December 1943. Germany is going to need a very large blue water navy to successfully reach the East coast with their unprecedented amphibious fleet. Many, many billions of DMs on shipbuilding.