Shortfall letter for voluntary class 3 contributions - how long to process

I have been trying to pay Voluntary NI contributions for more than 18 months. I originally applied in December 2022 to pay Class 2 voluntary NI contributions as I have been working overseas for many years. That application was processed, however, I was informed that I needed to resubmit the application, requesting Class 3 voluntary contributions instead. My new application for Class 3 contributions was submitted in August 2023 and was marked as Complete on my portal in March or April 2024. Whilst on vacation in the UK in June, I phoned the HMRC helpline to follow up on this application and was assured a shortfall letter informing me how to make payment would be sent shortly. I have still not received a shortfall letter and am therefore unable to make payment. How long does a letter normally take to process? Should I follow up again via the helpline or is there simply a backlog with processing shortfall letters?

Hi Seeking Solution,
Thank you for your enquiry.
The timescale for processing your application received in August 2023 has now passed.
Please contact the National Insurance helpline to ask for an update on your application.
The number to call is +44 (0)191 203 7010 (if you are calling from abroad) or 0300 200 3500 if you are calling from the UK.
Lines are open from 8am to 6pm, Monday to Friday.
Thank you.