HMRC self assessment

I am trying to submit my HMRC self assessment. I had an accountant do it for me last year but I feel they charge way too much for my needs. I have a full time PAYE job and just need to declare a small amount of rent received from a BTL property. I can provide a spreadsheet with rent received and associated expanses.

My accountant has a agent login to do my returns online. I tried to register with HMRC self assessment in Nov 2018 to do it myself but there was some discrepancy with my DOB and they needed me to send certified proof of my DOB which I did but it takes 6 weeks to process this and it still hasnt been sorted. I am trying to chase them up but its very frustrating.

I wonder given my current accountant can still file my returns with their agent login, would it be possible for another agent to file them on my behalf with same log in details (hopefully at a much cheaper price)? or could the new agent apply to do this and if so what is the process and how long would it take? (obviously with deadline for submitting approaching)

Thanks