Firstly, Dixie Station only existed for 16 months from May 65 to August 66 and only for a single carrier, so that's probably not an option. Secondly the RAN proposed the use of the HMAS Melbourne in March 66 to cover an ASW shortage at Yankee Station and the USN requested her in April 67 for the same reason, so there was scope for the employment of a non USN carrier on Yankee Stadium. Thirdly once Rolling Thunder ceased in October 68, after being limited in March 68, there was no bombing of the North until March 72, so that's not an issue for 3 1/2 years.
So I'd say the RN could easily find employment for one of their carrier on Yankee Station if it was offered to the USN. I think maybe after March 68 the squadrons would be changed somewhat, the Sea Vixen sqn made smaller and the Buccaneer sqn reinforced in light of the limited air threat.
I think the biggest issue would be the time the RN ships could spend on the line, like it was for the Melbourne. USN ships did ~31 day patrols on the line and their operational tempo was based around this, but of an RN carrier couldn't do the same (the Melbourne could only do about 10 days on the line) then it throws out the whole Port-transit-Line-transit-Port rotation schedule for the other 3 or carriers in TF77.