UK Employer unwilling to apply Swiss A1 certificate

I'm Swiss domiciled and resident, and a UK citizen and non-tax resident (never been tax resident resident). I'm currently working via UK umbrella payroll on a short term contract. Swiss social security wants a form signed by me and the payroll company in order to issue me the A1 certificate, as I will remain covered by Swiss social security and obligated for those contributions. However the UK umbrella payroll company advised they are unwilling to accept an A1 certificate (from anyone, not just me) and will proceed with UK NI contributions. I advised the Umbrella Payroll that the UK Swiss social security reciprocal arrangement states they are responsible for my Swiss Social Security, and they say they are only responsible for NI contributions. They know I am Swiss resident and understand that I am not covered by UK NI. What are my options here? 1. Pay NI contributions, and request a refund after the tax year ends. 2. Any way to get my code changed direct by NI themselves, so the code provided to the umbrella payroll would not deduct the NI? As it stands I may need to fund Swiss contributions + pension out of pocket equal to 20-30% of the gross for the duration of the contract. Net of the PAYE/NI/UK pension, my net payroll is around only around 40% of gross, before the Swiss social security. I will also approach Swiss social security to see if they will grant me a waiver until I get my refund in 2025 but seems unlikely.

Hi,
Please write to HMRC to request a liability decision. Please include the following information in your letter:

•    your full name
•    your National Insurance Number
•    your date of birth
•    the date they left the UK - if applicable
•    you most recent UK address
•    your address abroad – if applicable
•    the type of work they do
•    their company name and address – UK and abroad
•    where their contract is
•    how often they work in the UK
•    your normal working pattern (the days, weeks or months they regularly work)
The address to send your letter to is:
National Insurance contributions and Employer Office
PT Operations North East England
International Caseworker 
HM Revenue and Customs
BX9 1AN
Thank you.