Other nations with SSBNs is something I want to try. I don't know if this is all that plausible, but here goes......
1956 - After Suez, the British commonwealth decides to work on the idea of their own independent nuclear deterrent. The Americans (and Soviets) soon find out, but the Brits make it clear that this force is just part of NATO.
1960 - The first American SSBN, USS George Washington, is successfully tested. The idea very much appeals to the commonwealth, and the idea quickly runs wild. The British order their own SSBN class to be built as part of the commonwealth program. Canadian PM John Diefenbaker is another enthusiastic supporter.
1965 - the first commonwealth SSBN, HMCS Vengeance, is commissioned. It is the first of four Vengeance-class SSBN, the last of which is completed and comissioned in 1974.
1966 - two milesstones. The latest in American SSBNs, the Benjamin Franklin class, first enters operation. That same year, the world's first gas-cooled pebble-bed reactor enters operation in West Germany.
The gas-cooled reactor appeals to Canadian researchers and they get to work developing the concept under the guise of Atomic Energy of Canada limited. Of course, the side project also exists to use the gas-cooled reactors to make for a silent power plant for submarines.
1974 - the last of the Vengeance-class ships, HMCS Satellite, is launched. It becomes clear that the USA is developing a new class of SSBNs. The first of the "726" class SSBNs is ordered, and intelligence is that this class with museums of everything else out there, as the 688-class attack boats did for attack subs.
The Canadians' first gas-cooled test bed reactor goes critical at Newcastle, Ontario, on September 21, 1974. It proves to be a full operational success. The reactor is soon deemed to be able to operate as a much smaller unit, and plans are drawn up for a new SSBN class.
1977 - existence of the Commonwealth SSBN project gets to the Americans, but figuring that the new class would have the upper edge, they ignore it. That same data gets to the Soviets, too. The Commonwealth, figuring after American involvement in problems in Eastern Europe is learned by them, kicks the program up a gear.
1979 - HMCS Vengeance is damaged by a Israeli patrol boat while on patrol in the Eastern Mediterranean on April 3. The Israelis claim it was an accident, but the excuse gives the Commonwealth a chance to kick the project of the SSBN up a gear. Four days later, USS Ohio, the first of the 726s, is launched in Groton, Connecticut.
1980 - On February 12, the second Commonwealth SSBN class sub is launched in Liverpool, Great Britain. The HMCS London is considered by all - including the Americans, to their shock, to be an equal to the Ohio class. A month later, a second of the Nation class, HMCS Ottawa, is launched in Halifax, Canada. Both are comissioned in 1981 and armed in 1982. 17 London class subs - London, Ottawa, Canberra, Wellington, Dublin, Birmingham, Toronto, Sydney, Singapore, Glasgow, Auckland, Montreal, Vancouver, Salisbury, Melbourne, Edinburgh and Nairobi - are built, the last being commissioned on May 22, 1994.
1982 - HMCS Canberra and USS Ohio meet for the first time on the first patrol for both. Ohio gets first blood when he detects a slight metal squeal, but rough water gives Canberra the ability to return salvo. The two boats both surface and congratulate each other, with Captain A.K. Thompson on Ohio and Commander Robert Allister on Canberra promising to buy each other beers and beat the crap out of each other next time around.
1984 - An Azerbaijani oil facility is blown up by terrorists, and the result is an economic crisis in the Soviet Union. A war results as the politburo tries to take the Arabian and Iranian oil fields by force. The Soviet Army attacks Germany but its commanders keep a tight rein on their missiles. The war stays conventional, but the Soviet Navy is sent out to stop help from getting to Britain. Sheep numbers of naval attack vessels help the Soviets keep an advantage in the Atlantic.
1985 - A starting-to-panic Britain want to order an attack with the SSBNs, but Canadian PM Mulroney and Australia's Bob Hawkes both convince Thatcher that this is unnecessary and that it will bring a much uglier nuclear response. But in July, this game changes.
Brand-new SSBNs USS Rhode Island and HMCS Vancouver decide via NATO communications to operate together to attack Soviet Subs. Both sides' bosses are shocked, but both Captains are convinced they can act as SSNs.
The two subs together take down more than a dozen submarines, which gives both Reagan and Thatcher the idea of using their "black hole" subs as both attack and missile boats. The idea is a success, with both boats only returning because they had run out of torpedoes. Almost immediately the entirety of both navies' submarines attacks the Soviet Navy, effectively shutting down the Navy war. Soon, the American and Commonwealth SSBNs join up, riding shotgun on each other. This tactic causes huge losses to Soviet Subs. One HMCS boat, Canberra, is damaged by a ramming from a Soviet Navy cruiser in an altercation and is sent to Halifax in order to be repaired.
1986 - The Third World War ends without a single usage of nuclear weapons. HMCS Canberra is examined in Halifax, and the Canadians decide to use it as a bed to test out a new idea. Commonwealth command agrees.
The idea would mean stretching the already-huge ship with a slightly wider center beam and a 125-foot beam stretch. The idea is to carry American AH-64 Apache and RAH-66 Comanche attack helicopters. The boat is refitted, as well as having 12 of its Ballistic missile tubes refitted to carry cruise missiles. Also included are an extra 42 berths for the helicopter crews (bring the total to 24 officers, 203 men) and fuel tanks for the helicopters. The most amazing feat of engineering is a carrier-style elevator and opening roof of the sub, allowing the choppers to be stored in the subs.
1989 - Canberra is recomissioned, and is a success. It's first tour in May 1990 also happens across the USS Pennsylvania, and the two commanders - Captain Thomas Mandelbay on Pennsylvania and Commander Eric Jackson on Canberra - play against each other. Mandelbay is shocked to learn that it was not another Ohio playing against him, but one of the HMCS boats.