It did depend on the scheme but from 1988 most occupational schemes would have been opted out as it meant the employer, and employee, paid lower NI so for the employer it reduced the cost of the scheme. In effect if RaindropsAndSparkles didn't opt out and Brasty did then Raindrops would have been costing the employer more. Before 1988 it was only certain schemes but for Raindrops most of hers would have been post 1988.
In your calculations you haven't allowed for the deduction that will be made for the year or years you were contracted out, even if you have 35 years without that year or years it will still be deducted.
If people have worked and contributed for 35 years without being contracted out they will get a full pension, if they have been contracted out they won't. I think it was Which that was doing a campaign to alert people to this . This is the sort of confusion that means many people think they will get the full new pension but in fact they won't.
Govt figures in answer to a freedom of information request by Hargeaves Landown showed that in the first 5 years of the new flat rate pension less than half of people retiring would get the full amount, some as they didn't have 35 years contributions and some who did but were contracted out.
It is some years since there was a fixed retirement date, people have been working till 67 and beyond for many years and some of them were also taking their SRP and some were deferring.
I think everyone should ask for a pension forecast, the calculations make for interesting reading. My entitlement to the new pension is less than £100 a week although I have over 42 years of contributions.