I realized after I replied that we may be looking at this from two different angles. I think you're looking at it as the Navy making an almost snap decision to keep the Essex class in service. Whereas I'm looking at as the Navy making a logical and informed decision. For example, the Navy says they need X number of carriers to fulfill their missions. Congress says they'll authorize Y number of carriers, but will only provide enough funding to build Z number of carriers over however many years. So that means the Navy will have to keep older ships in service to meet Y until the new build ships come online. Obviously it's not ideal, but at that point, the Navy is going to make the best of it and try to make what they have as capable as possible. Or at least that's what they'll do once they realize Congress is serious about not funding their wish list.
I can also keep Essexes in service in the support carrier role into the 1980s, which meets part of the OP.
In the middle 1960s the USN had 25 active aircraft carriers, made up of 15 CVA, 9 CVS and the training ship. AIUI the plan was for this to reduce to 22 ships comprising 15 CVA, 6 CVS and one training carrier by 30th June 1975. The reduction in the number of support carriers was because the P-3 Orion had made them redundant in their current role, but the improving capabilities of Soviet submarines meant that a smaller number of ships was needed to protect the attack carriers.
Requirements were based on the "rule of three". That is three ships were needed to maintain one forward deployed ship at all times. They wanted 3 attack carriers in the Western Pacific and 2 in the Mediterranean, which meant that 15 were required to maintain 5 forward deployed ships. They also wanted one support carrier in the Western Pacific and another in the Mediterranean, which produced the requirement for 6 support carriers.
The plan was that the SCB.27A Essex class (of which there were eight) operating in the CVS role would be replaced by SCB.27C ships (of which there were seven) that were being replaced in the CVA role by the new super carriers. The SCB.27C ships would in turn be replaced by SCB.100, which was a purpose built CVS. In September 1963 the plan was to order the first SCB.100 in the Fiscal Year ending 30th June 1968. However, this had slipped to FY1971 by April 1964 and this version of the design could not operate Phantoms because the C-13 catapults in the SCB.101.68 design had been replaced by less powerful (and cheaper) C-11s. This version of the design wasn't built either and Intrepid the last Essex operating in the CVS role decommissioned on 30th March 1973.
AIUI the VSX which became the S-3A Viking was designed to operate from SCB.100 and Essex class ships refitted to SCB.101 standard. The 187 aircraft that were built were to provide a front-line of 120 aircraft in 12 squadrons of 10. That is 2 squadrons per CVS.
So another POD could be that Congress provides the cash to maintain the 22-carrier force and the money to have a force of 12 "supers" and 3 SCB.101 Midways by 1975, but the Essex class have to be given a SLEP refit because the money to build new support carriers won't be available until the 1970s.
IOTL 8 Essex class carriers were given a refit designated SCB.144, which was part of the FRAM II programme and were funded FY1962-66. Lake Champlain was to have been refitted to this standard in FY1966, but it was cancelled by Robert McNamara. All but one of the ships that had the refit had previously been modernised to SCB.27A standard, the exception was Intrepid, which was a SCB.27C ship.
Therefore, ITTL SCB.144 waa FRAM I refit and the refit planned for Lake Champlain was carried out.
AIUI FRAM I refits were intended to extend a ships life by 8-10 years and FRAM II refits were intended to extend a ships life by at least 5 years. (Source, Destroyers by Anthony Preston.) This version of SCB.144 would include fitting steam catapults powerful enough to launch the C-2 Greyhound, E-2 Hawkeye and S-3 Viking, plus the flight deck, lifts and arresting gear would be strengthened if that was required.
By the late 1970s they would be operating an air group of 45-50 aircraft, which would consist of:
- 20 S-3A Vikings in 2 squadrons;
- 16 SH-3D/H Sea Kings in one squadron for ASW and possibly 2 or 3 SH-3G Sea Kings for SAR and VERTREP;
- 4 E-2C Hawkeyes
- 1 C-2A Greyhound
- 4 F-8 Crusaders to give the ships an anti-shadower capability.
This was the air group planned for SCB.101.68 except that 4 Phantoms would be embarked instead of 4 Crusaders.
The 9 ALT-SCB.144 ships weren't official CVAs, but they retained their attack carrier capability, which could be used if more CVA's were needed at short notice. The air wings would be provided by mobilising the 2 Naval Reserve Force air wings or embarking Marine squadrons. I don't see that happening if World events were the same as OTL, but the NRF air wings and Marine squadrons would be embarked on the ALT-SCB.144 from time to time as part of their regular training.