HCLF should be doable. I'm already on insulin (too much for my peace of mind) and Metformin. Metformin has caused problems for my stomach and bowel for years now, but I had to make a choice (ie no metform, high bg v 3 metformin daily and stomach/bowel problems) and opted for what I thought was a safer route of keeping slightly better control over my bg. I don't think the Metformin has caused my gastritis, but possibly Esomeprazole, which I was put on many years ago and which has never been reviewed, might be the cause.
Iron supplements also cause severe stomach problems and last time I was diagnosed with anaemia I had to have iron infused. I'll be asking the Dr about that next week, when I finally get to see her.
Any ideas for a HCLF diet?
I totally agree, better Metformin than higher bgs. This probably won't help you, but in my case I had terrible digestive / reflux problems for years, which were helped enormously when I began eating low carb. Previously I had had two endoscopies, which showed nothing except that I was developing a small ulcer. My GPs wanted me to take a med in the Esomeprazole family, but I refused. Instead I researched for the least risky med that might help and found Peptac.
https://www.netdoctor.co.uk/medicines/digestion/a7328/peptac/
This helped a lot at the time, but since I started low carb I have not needed it once, and I asked my GP to take it off my repeat prescription list. I do still have some problems with bloating, but given that I am taking Metformin AND Dabigatran, both notorious for causing this sort of effect, I think I just have to make the best of it.
Good luck with the HCLF diet. I don't have any ideas to offer, and anyway I fear it would be too painful for me to dwell on asll those lovely carb-filled foods I no longer eat! But do let us know how you get on.