Switching to Salary Sacrifice Pension contributions through nest

Like many on here (judging by previous threads) we have our co-op pension scheme with Nest and we work out our payroll on the HMRC RTI system.

While looking at other stuff on the web I stumbled upon the concept of salary sacrifice schemes and by extension salary sacrifice pension schemes.

I was wondering if anyone has set this up with a standard nest pension and using the HMRC RTI software.

To be honest I am not sure I really understand it but I THINK it would go like this.

If you earned £24000 a year (£2000 a month) you would opt to sacrifice 5% (your pension contribution) of your salary so £1200 (annually) meaning that your contracted salary would be £22800 (£1900 a month). You are then paid £1900 through PAYE rather than £2000 and the company pays your sacrificed 5% + their 3% of your salary in employer pension contributions and you pay 0% (this could be set up automatically using groups in NEST for those that wanted to join the salary sacrifice pension scheme

I assume that you could opt to sacrifice 10% and the co-op would pay 13% of your £24000 salary contribution . I also assume that you could opt to sacrifice 5% and still pay another x % in on payday as normal. Actually, Due to the wierdness of percentages I think that if you were to sacrifice 5% you'd want the co-op to pay 9% not 8% and if you sacrificed 10% you'd want the co-op to pay 15% not 13%) you can see some workings here https://lupineadventure.sharepoint.com/:x:/s/LupineAdventureCo-operative/EQ6Iuez_Q7FBgV1bH7RThYoBvrh6foIa-cbAEkqWtxNvtg?e=CbmXaS

The advantage (I think) is that there are no employer or employee NI contributions on an employers pension contribution (so both the co-op and the employee benefits). The disadvantages seem to revolve around your pay is less so if you wanted a mortgage it would be less or if you were made redundant it would be less (and other things around qualifying for certain benefits like levels of maternity pay).

How much would it save?... Well if my calculations are correct. I think that if an employee on the salary above did this and sacrificed 5% a year (i.e the minimum for auto-enrolement contributions) they would get an extra £12 a month in their pension and the co-op would save £13.80 a month in NI contributions. If they sacrificed 10% they would get an extra £24 a month and the co-op would save £27.60. They are quite small numbers but for the individual we are talking pension time frames so £144 a year (or £300 for a 10% sacrifice) extra in a pension pot. And for the co-op we could be talking about multiple people opting to do it. In my co-op we nearly all pay more than the minimums in to our pensions so it would add up to between £500 and £1000 a year we wouldn't pay in employer NI contributions

So my questions are

1) Has anyone done it?

2) Is my understanding of it (above) correct

3) Any other comments