Would you say carrot fiber is the most reliable and safest? I have dropped dairy also and found it has helped a number of issues. Do you think you could add other fiberous vegetables like broccoli perhaps, although not peaty....I find it agrees with me when well cooked.If I had to guess what's causing the hairloss based on the dietary template you described I'd say it was the dairy. Dairy is high in quite a few hormones including estrogen, 5ar reduced steroids, progesterone and others. Its also contains opiates that can increase prolactin and lower dopamine. These factors overall can possibly lead to increased prolactin on your blood test which lowers your testosterone and/or push your test towards dht. I've only seen a select group of people tolerate dairy well, many others are hormonal nightmares from it.
On a practical level I think experimenting with dropping all dairy would be worthwhile and replace it with meat, select seafood and eggs. I'd broaden the range of whole fruits you where taking in, as well as 100% juices and salt to taste, no need to add large quantities of salt. As for fats I'd use beef tallow, chocolate, cocoa butter, and coconut oil. Butter wont have the opiate effect but it will have the hormone effect. I'd also add in a carrot with each meal or so for some fiber to keep your regular (in conjunction with the whole fruit).
In order to regrow hair, I have seen some good reports with microneedle with a 1.5mm derminator every 2 weeks. I'm not a fan of the pharma drugs currently available for regrowth, the side effects and mechanisms of the drugs are often problematic and a bit risky in many cases.