I was never on animal insulins and glad that I never was. I would say that preservatives and other ingredients to remove unecessary items from insulins make both animal and recombinant insulins unnatural. Different people react to insulin and other ingredients in the bottle differently and it is possible that recombinant insulins are causing you problems, but it is not likely. Recombinant insulins have reduced adverse events, allergic reactions and lithotrophy more commonly associated with animal insulins.
I would argue that Recombinant DNA insulins are more natural than animal insulins for you. scientist have identified the human genetic sequence required to make the protein insulin. They have then inserted the insulin DNA into yeast cells and the yeast make the protein insulin. You can then harvest the "human" insulin, purify it and use it. since recombant insulins are made to be just like normal human insulins, I believe they are more natural for me than animal insulins.
Through trial and error, scientist have found ways to make the recombinant insulins more useful or predictable. For instance, removing the c-peptide increased how quickly the insulin became active and lead to much better bolus insulins. Lantus is made to a pH of 4 (quite acidic) and this causes the insulin to be absorbed very slowly and predictably, good quality in a basal insulin. And more recently scientist changed 1 or 2 of the 51 amino acids in regular insulin. This changed the tertiary shape of the insulin a very small amount, but lead insulin becoming active much sooner. It was named humalog.
I have often wondered if there would be noticable benefits from taking c-peptide as a supplement though.