The most likely way to have Franco join the Axis is to have him think that they were very close to winning the war. Maybe we can do something like my Return of the Tsar tl, where Hitler dies early in the invasion of the USSR, and a more practical leader (in my tl Goering) becomes Fuhrer. With a slight change in Soviet attitude to the USSR, the Germans are declaring the invasion a war of liberation, even setting up a puppet government (in my tl a surviving Romanov).
Russians are divided, but a significant enough percentage of them rally to the new Tsar and play a vital role in "liberating" Leningrad and Stalingrad. With the war on the Eastern Front looking like yet another German victory, and with a Fuhrer who is more rational, Franco offers a Spanish alliance to Germany in hopes of gaining some spoils of war.
Eventually I believe the western allies are going to invade Iberia, and though Spain may become a meat grinder, the western allies eventually win. How this goes from here is beyond me, I never got that far. Russia is embroiled in a brutal Civil War with the western support Soviets against the German supported monarchists. This frees up some German troops, perhaps even enough to thwart or slow down an allied invasion from the west, turning Italy and France into meat grinders as well. The allies may be able to go with the Turkish option, and twist Ankara's arm to get them to join the allied cause. The Balkan front becomes a major operation for the allies who initially catch the Germans off guard.
Also expect an earlier allied invasion of Norway
I mostly agree with you, but note that a more rational Fuhrer is not even neccesary... it would be enough with a more rational Franco.
OTL, Hitler ad Franco reunited in Hendaya to deal the conditions of Spain entering the war. The problem was that Franco demanded too much (a good chunk of Africa and too much material and logistical support), which angered Hitler. Some people argue that Franco subtly forced Hitler to that decision, but they tend to forget that the Hendaya reunion happened when the Axis seemed unstoppable, and the distinctive totalitarian and anti-liberal flavour of the early Francoism (that evolved into a simple anti-communism and a "it wouldn't work here" stance on democracy, when the cold war logic made it neccesary). If Franco had made more sensible demandings, maybe Spain would have entered the war.
As for the results... well, it is obvious that it would not make the Axis to win, as the Spanish army and industry was in a terrible state... some forum members think that, instead of delaying the victory, it would have make it easier, as it would have given the allies a good continental stronghold in shorter time... I'm not realy sure about that. It would be interesting to think about the butterflies it would cause in the postwar, though. Specially in the axis side, and in Spain... it is easy to consider a liberated postwar Spain with an stablished conservative democracy with alienated far left parties.
As for Portugal joining the axis... that is really, really hard. Not only the Portuguese would have no reasons to stab their long-time British allies in the back, but the Salazar regime had no great ideological resemblance with the fascist and nazi regimes, apart from being undemocratic and corporativist. Even Francoism had a greater fascist façade then, the Salazar regime being mostly reactionary and openly hostile to some fascist and nazi "revolutionay" premises. The No Spanish Civil War TL, by Dr.Strangelove (read it, Nusantara, it goes far beyond great) has a Portugal joining the Axis, but the circumstances described are very different there.