Next steps to gain ILR

Suggestions appreciated as to our next steps to gain ILR…

My same-sex partner arrived in the UK in 1998 and immediately claimed asylum. His case remained unprocessed for 6 years and was then refused, as Kosovo is now deemed safe. We withdrew the asylum application at appeal and successfully argued ECHR article 8 and he was awarded Discretionary Leave for 3 years.

We now seek to get ILR as soon as we can. The following appear available to us…

Unmarried partner – we have been together for two years (I have right of abode in UK)
HSMP – he is a UK qualified Doctor and has enough points
Permit free training – he is in the last year of GP training and still qualifies
Long residence concession – he is nearly at 7 years and I believe discretion is available on the 10 year rule
Naturalisation – he meets all criteria where discretion is allowed however, I understand his Discretionary Leave being time limited may be a problem.

Other potentially relevant facts…
He is employed by the NHS and working as a doctor. He has broken no laws so is of good character. He speaks English – surprisingly as a doctor, and he does not hold a passport of any kind (UN in Kosovo do not issue passports to non Kosovo residents)

Any suggestions as to our next step are greatly appreciated.