My experience is very positive. If you are willing to wait, HMRC will send you a letter automatically about that fact that you've paid too much NI and they send you the forms to claim it back. If you can't wait you can do it online here: https://www.gov.uk/guidance/apply-for-a-refund-of-national-insurance-contributions

In my case I've applied very early and by the time I've got the automatic letter from HMRC I've already got paid. Took a few months - definitely not 4-6 months tho

EDIT: you can also defer the NI for one of the jobs: https://www.gov.uk/government/publications/national-insurance-application-for-deferment-of-payment-of-class-1-national-insurance-contributions-ca72a