Waiving away the 1943-44 S Pacific offensives, and postphoning the Central Pacific offensive would cover part of the overhead. The problem was more for cargo shipping to move the pre and post invasion material, or build up. Even if enough landing craft are present for the task the global cargo fleet must be rearrigned as well. Things like reducing supplies to China, USSR, ect makes another big chunk of cargo capacity available.
Ground combat forces is not a big issue. Op DRAGOON was executed with units that had been in the MTO since 1943. Perhaps one of the French divisions would not have been ready, but thats a open question.
Nothing changes for air power. IN January 1944 the Allied air forces out numbered the Germans by a incrediblly huge margin. The air bases in Corsica/Sardinia were ready months earlier. Maybe operations over Italy would be reduced a bit to do the air operations supporting a June DRAGOON Op
Note that Eisenhower had badly wanted a ANVIL operation in April. Expanding Op NEPTUNE from three corps/beaches to five made Op ANVIL in the spring impractical, but Ike kept HQ staff at SHAEF & SACMED busy in January & February trying to make it work. He finally canceled Op ANVIL in March, much to Churchills delight, then Ike imeadiatly ordered the operation revived with the name DRAGOON. Churchill was beside himself and argued against Op DRAGOON right to the last moment. Brooke did not seem to care for it either & only a couple of British brigades of commandos & paras participted.
On the game board I extensively tested a earlier ANVIL/DRAGOON operation. Ikes April 1944 target I went through several times, and a January or February date multiple times, plus the May/June window. In all cases I presumed not more amphibious or cargo shipping than OTL, so the NEPTUNE & OVERLORD ops had to be scaled back. If the ANVIL Op came in January February I reduced NEPTUNE to a four beach/corps landing, if ANVIL came in April - June Op NEPTUNE was reduced to a three beach/corps landing, as per the 1943 COSSAC plan for Op OVERLORD/NEPTUNE. In the last case I also moved Op OVERLORD forward to May, as Montgomery originally planned.
To make the January/Feb AVIL op work I assumed the Anzio landing Op SHINGLE was canceled. That made more US forces available for ANVIL, but also allowed some of Kesselrings reserves in Italy to be transfered to France.
Whatever the date of Op ANVIL it benefitted the Allied side. The German player had a array of choices to make, none of which were good. If enough reserves were sent south to deal with the Allied 6th Army Group then north west France was left too weak & even a reduced OVERLORD had a lot less trouble creating a large lodgement in Normandy. If only a holding action is made in the south the Allied player can build 6th AG into a nasty powerfull force and weaken the German position in south France to the point of collapse.
Best course for the German player was to strip Kesselrings Italian front of all reserves and reduce the 10th Army to a delaying force. That gambled losing the Gustav Line in 1944 & the northern industrial region of Italy, but it helped with providing some mechanized and horse mobile corps for France. Still the invariable result was the Allied player being a month or three ahead of the OTL positions in the Autum of 1944.