Mmm...do you mean to say that the likelihood of the goverment imposing restrictions on the immigration of software developers is kinda slim?
No, but compsci/software is an in-demand field so if there are things like NOC-based draws in the future, you may be on the better side of it. You're too hung up on "government imposing restrictions". You need to face realities and plan accordingly. Despite the liberal party's increased immigration levels, it is no surprise that Canada will be reducing the quota for skilled immigration. In fact, they already did. 50% of FSW's quota is transferred to other streams, although temporarily. This gives out a message telling you that FSW is the first to be chopped up if things change. In my opinion, not acting now and trying to figure out what would happen half a decade later is a bad plan.
If I were to use my data analyst experience, what documents would I need to prove it? Will a reference letter from my ex employer suffice? I don't think I would be able to find any salary slips now. It's been years since I left that job.
Gonna have to do your homework (easy homework though, look at IRCC's website, it's all there), but typically you need to provide a work reference letter. The appropriate format of the letter and what IRCC wants to see on it is again on IRCC's website. Google it and you'll find it on IRCC's website.
You don't have to select data analyst as your primary NOC, you can select the other one too (given that it's NOC 0, A or B and you have completed 1560 hours in it).