It sounds to me like the modern process is just working up GMO yeast matabolites. I feel like the main issue is probably going to be patents and not something technical.
Edit: Answering myself here, they do not: https://www.vorys.com/publications-2574.html
However, many patents that are issued in association with a research grant include a clause that allows the government to use the patent without charge. I have no idea if any/many insulin patents are included in such clauses.
Now, if you closed the loop and used older insulins, you'd have good control and less issues since a computer would bear the cognitive load, but glucose control, especially in the outpatient setting, is ridiculously hard. If you think you can solve it though, give it a shot. It's a multi billion dollar market and a lot of lives you can improve.