Self-assessment student loan repayment

rotparoge

Hey, guys. Wondering if anyone could help with information here because I've hit a wall with HMRC and SLC. 
I'm self-employed and I've been paying my student loan back through self-assessment. I filed 2019/2020 return in summer last year and paid my balancing payment once I'd done that well ahead of the 31st January deadline. My student loan repayment was more £4424, which is more than the amount I actually owe, so I got in touch with SLC to ask them when their system will update and show that I've cleared my loan off. They told me to speak to HMRC and ask when because they couldn't tell me. So I spoke to HMRC and they said they received my payment ages ago and it's all automatic once they've received payment. I contacted SLC again to see if they could at least offer guidance on when it will appear in their systems. They're now saying it could be at any point this year. 
Does anyone know when this is likely to be? I read on MSE that HMRC and SLC are now supposed to be updating each other weekly. Just wondered if that's only for PAYE. I'm not in a rush to claim my refund. I'm more interested in getting confirmation that my loan is clear.