In my opinion (and I'm not an expert), the major problem with the WIF was twofold. One, there was no real pan-Caribbean identity.
There was and still is to an extent. The cricket team had been formed long before the federation came about and was formed before WWII.
Two, the government was quite federally centralized, making it logistically difficult for the already divided federation to survive.
Back in university I remember there were some books on it and I got to peruse a couple. Essentially the problem was that it was not centralized enough. It started out as being a relatively strong federation in concept in the late 1940s to mid 1950s but then the territories that were due to make up the federation progressively got more self government until some were more autonomous than the federation was planned to be and at the same time the progressive weakening of federal powers made it less appealing to the top politicians hence they didn't bother to enter federal politics.
Here is my plan:
During the Second World War, the British decide to organize a "Caribbean Corps", calling on men from across their Caribbean possessions to join the British military and fight for democracy.
Britain beat you to the punch:
http://en.wikipedia.org/wiki/Caribbean_Regiment
Doubt you could get that many. In a population of 3 million, you would probably be looking at a maximum of 20-25% of the population being in the right age group (18-50) and of the right sex (male) for military service. That leaves a pool of 750,000 but then out of that you be lucky to recruit 10% to leave to fight in a war when the danger isn't near and you haven't imposed conscription.
Even with Australia it had a population of about 7 million in 1945 but had 724,000 personnel who served throughout the war with conscription. So using Australia as a model at best maybe 300,000 West Indians could have been conscripted, but without conscription getting 80,000 would be tough. Even in Australia and Canada volunteers were not overwhelming. The 2nd AIF was an all volunteer force and it initially consisted of 20,000 soldiers before having its ranks swollen once Japan entered the war and the danger was a lot closer to home for Australia. With Canada there were enough volunteers for 5 divisions to serve overseas in 1941 out of a population of 11.5 million. Assuming these 5 divisions numbered about 75,000 then that would be about 0.65% of the population.
Using Australia and Canada as examples then we could expect between 0.28% and 0.65% of the population to be volunteer men for your Caribbean Corps (or our OTL Caribbean Regiment). This would equal anywhere between 8,400 to 19,500 West Indian volunteers. The Caribbean Regiment had about 1,200 soldiers but in all 10,000 West Indians volunteered for the British forces so the West Indies definitely falls within that range, if towards the low end. From what I understood there was a general reluctance on the part of military command to have the Caribbean Regiment take part in fighting as well and more West Indians saw action with the British and Canadian forces than they did with the Caribbean Regiment.
After the war, as these men return home, some find leadership positions in their communities,
Many of them did in OTL from what I read. Norman Manley (one of the politicians behind the federation from Jamaica) served in the First World War and his son Michael Manley served in the Second World War. There was also this fellow Marryshow from Grenada who was way too old to have served in either World War but he had a nephew or a son or something who fought in the Second World War (in the RAF I think).
as many of them have become educated due to the Veterans' Support Act.
Most would probably have been educated before. With conscription you could probably get this to occur, but with a volunteer force there will still be requirements (including educational requirements) which would have to be met first before someone is allowed to enlist.
When the West Indies Federation (WIF) is formed, these men have become influential in their nations' politics
Those men might be too young. If they served in the Second World War they would have been between 18 (maybe 16) and about 50 between 1939 and 1945. The federation was formed in 1958 (13 years later) but had been in the formative stage from as far back as 1947. So in 1958 some of these people will be about 37 and almost certainly not be influential in politics at the time as there would be older, more well established and well known politicians in their way.
From the couple of books I read it seems thatthe easiest way to get the federation to survive would have been for:
(1) the retention of the temporary provision which would have allowed politicians to serve in both their provincial/territorial legislature and the federal legislature at the same time for the first 5 or so years of the federation's existence.
(2) the federal government to have retained more of its original powers including some amount of taxation
This would have given more importance to the federal arena of politics and allowed the top politicians to basically "graduate" to that level and take their support base with them. Once firmly established at the federal level these politicians would then be unlikely to set their sights on going back to the provincial level of politics again (in an independence bid for their specific provinces), plus newer politicians in the provincial legislatures would not be keen on having themselves displaced by the returning politicians and would also set their sights on federal representation (thus seeing provincial politics as a stepping stone). It would also have given the federal government an independent means of revenue rather than simply relying on the provinces to contribute to its budget.