Sorry i really never cycling my tanks and i don't understand cycling and i don't like to use anything besides just water conditioner . I think any extra product has some kind of chemicals and can do more harm that better. So i would rather change water a lot then use anything. Even if it organic ....
And how i understand that his tail was getting better with daily water changes and stopped healing when you use purigen? Because his tail looks good even if it not fully growing still looks good and i would think that if you did daily water changes last week that is exactly what helped him. So this is the answer not sure how big is your tank but i would recommend to do 100% water changes or 50% and 100% weekly.
Did you see those links? I am going to post amazing links from this forum for you. Actually 2 links when people did 100% water changes and how much it helped.
see page 1; page 43 #422 and see page 42 and page 52 Amazing right!
and i can give you anothre link if you want about frequent water changes. I think it the best. I don't have any problem with my betttas whatsoever with 100% changes. Of course need acclimation. If you will make sure new water temp the same as his when you do 100% changes and if you will take time to acclimate him buy adding new water in his cup and let him used to it you should not have any problem. If you have hard water you should take longer time to let him acclimate to the chemistry