What about specialized aircraft? Something like lots of cheap amphibious aircraft, so maybe biplanes, being small and light enough to land on a beach or just offshore in sheltered waters? I am assuming that you want airpower right on the initial landings, functioning in close air support role, that then stays throughout the entire operation, while carrier aircraft are going to stay with their ships most of the time, and other land based aircraft are going to be spending time going to and fro from their airfields.
If you went with low capability aircraft like amphibious bi-planes, they can operate from tenders, which being far less of an investment could perhaps be left in situations where a fleet carrier would not be. With the low speeds and very nimble characteristics might make a very useful combination combined with large numbers of very cheap aircraft that really cannot be used for to many other missions, and thus wouldn’t be taken away from their intended role. Any more capable aircraft types would either require a nearby carrier or airfield, and would likely not be kept to the dedicated invasion operation.
So for instance, at Guadalcanal, give the Marines a tender or three, and matching squadrons, so even before the airfield is captured and completed, the invasion can have its own dedicated CAS. Taking it a step further, a dedicated tender that is beach-able, and/or has a ramp for amphibious tracked vehicles to swim ashore and carry all the munitions, fuel, and maintenance folks with their tools and such, then even the tenders could be withdrawn, and still leaving the invasion with tiny aircraft that can go ashore practically anywhere, be dispersed and concealed from enemy land based and carrier borne raids, and as they really couldn’t be used otherwise, will be left to their task.
Another benefit, as such aircraft would be taking large losses and cost less than more capable aircraft, you could see their being a good replacement rate built in to offset the expected heavy losses, and thus ensure the forward based units have reinforcements available, if they can just be delivered. Also, is it possible to build such a force from non-strategic materials, so steel and wood/fabric?
None of this precludes the OTL marine aircraft, but would provide the niche for CAS without the need to expose the Carriers for the duration of the operation.
One additional thought, if taking this to the extreme, what if in addition to the above posited tenders, you have some dedicated craft capable of bringing engineering vehicles and equipment ashore with their own amphibious vehicles, making construction of forward airbases somewhat faster?
Would this type of thing fit the bill?