Did you get a summary decision on the day or were you told the decision was not being given on the day and it would be in the post? DWP do not need anything but the summary decision to put benefit into payment.
If you won, why do you need a SoR/RoP? Is this because you think the award ought to be higher and wish to challenge it?
Aha, so DWP could put benefit into payment but have elected to not do so as they're awaiting the SoR from the judge in order to consider an appeal to the Upper Tribunal.
They could be pressed for payment but their counter argument will be that were they to ultimately win the case then you will have potentially been overpaid and it would not be recoverable so, better to not pay out in the first place. Not saying I agree but that's what their argument will be.
The judge has a deadline by which they need to produce such documents but whether they hit that will depend on the volume of similar requests and whether they are salaried or fee paid. There's obviously an incentive for the fee paid to crack on with such things but it doesn't always work out like that.
It's a judgement call and there's no "right" advice in such situations. A complaint to HMCTS may kick things into gear but equally you don't want to rush a judge into doing it quickly if details are then recorded incorrectly. I would suggest it's best to sit tight and see what happens next, frustrating as that may be. You may feel differently.