Applying for settlement in the UK while holding a Discretionary leave (DL) visa after being refused an asylum [closed]

I am writing this on behalf of my family and myself. My mum, sister and I visited the UK in 2011 and due to unforeseen circumstances could not return back to our home country. We were then left with no choice but to apply for asylum fearing for our safety. After several refusals by the Home Office we were granted a Discretionary Leave to Remain on July 2017. Our visa is due to expire at the end of 2019 and we are looking to apply for settlement as we have been in the UK since 2012 and have deep roots.

My question is, has anyone applied for a settlement visa/status by having the (DL) visa and what the process is? I also would like to know if anyone knows if the chances of applying for an extension of stay and getting accepted would be higher than applying for a ILR or settlement status.

I personally am looking to settle as I have done my GCSE's, A Levels and obtained my university degree in the UK. I am also working in Finance and a soon to be a Private Banker. I have met incredible people in the U.K and have deep connections with many friends and a soon to be fiancé.

Thanks!