Actually, through as late as 1944, the CVL's formed as much as 40% of the striking power of Spruance's fast carrier groups. So actually, they WERE at the forefront of Nimitz's strategic offensive of 1943-45 - they were just *part* of the force structure, not the sole basis of it.
I mean, they were integrated right into them, because they were fast enough (31.5 kt) and could accommodate any of the Navy's standard fighters or bombers - and they were, above all,
available. The typical OTL four carrier fast carrier group had a mix of two CV's and two CVL's. This is basically what
the U.S. Order of Battle looked like at the Philippine Sea.
What this means is that early on, the CVL's would just form a somewhat higher percentage of the decks. For example, let us say Roosevelt authorizes an additional 6
Independence class conversions in June 1942 (he had already authorized all nine of our history between January and May of 1942).
- If Nimitz is in a bad pinch in the spring of '43 - say if Yamamoto is trying a new offensive - the only Essex on hand would have been, well, Essex herself. But this expanded Independence program could have given him 6-8 CVL's to complement his few CV's at that point. That could make the difference between being able give battle in a major carrier engagement, and not being able to.
- By November 1943, this expanded CVL program would give Nimitz 5 Essex class carriers, 15 Independence class light carriers, and Saratoga and Wasp, if they survived to this point. What you could do then, would be to assemble five or even six 4-carrier fast carrier groups, each one built on one Essex (or Saratoga/Wasp) and 3 CVL's. Granted, the striking power of these groups would be modestly less than Spruance's 2/2 groups of OTL, but they're better than not having them at all. And the Independences wouldn't be on their own.
And as more
Essexes come online, you adjust the composition of the carrier groups accordingly.
Meanwhile, the CVE's just get used for close air support or ferrying aircraft, as they were OTL.
So no, more
Independence class carriers cannot be the
sole answer here, but they are still the only way you can get more fast carriers (I mean, over and above what was already on the slipways) into the Pacific in 1943. Converting an
Alaska is not an answer here, because none could have been available as a converted carrier until mid-1944. Which *I* (and Calbear!) might do anyway, but only because they'd at least be useful for something toward war's end.
There are no other slipways that are big enough to build an
Essex available in mid-1942, beyond the ones already in the processing of constructing them.