Long Residence (10 years) Advice Needed Please

[Tvkumar]

Hi, need advice if possible. I am thinking of applying for ILR. My status history as below.
09/10/2003 - 31/01/2005 - entered UK on student visa
22/02/2005 - 31/07/2005 - extension based on thesis
27/10/2005 - 28/02/2007 - student visa
24/05/2007 - 30/04/2008 - student visa
18/04/2008 - 18/04/2009 - International graduate scheme
12/05/2009 - 18/04/2010 - International graduate scheme
12/05/2010 - 12/05/2013 - TIER 1 Migrant visa
10/05/2013 - applied for visa on family grounds. Daughter British national. Rejected in June 2013. Appealed via solicitors. Rejected again. Went to tribunal and won the case. Received residence permit on discretionary family grounds. Issued 03/07/2014 - 03/01-2017 with a view to apply for another two and half years on the same basis. The whole solicitor process was very painful and ridiculously expensive. Throughout my stay I never overstayed my visa. Any gaps in the above dates were due to the ridiculously long visa processing times at the Home office.
I'm sick of applying by post and would prefer to go in person if possible. I need frequent travel on work so can't afford to send my passport for months. I am not sure what documents I need to produce as proof. All the visa stamps are on my old passport which I still have with me. Don't really want to go to another solicitor without doing ground work.
I did the life in the UK test. My stay outside UK has been within the allowable limits.
Any suggestions on how I can apply for ILR would be very much appreciated.

Thank you in advance.