If you want to rush and do it now then:

You can get 1,300 a day if you clear all 12 trials. If you buy the fragments twice a day for 1,000 each then it'd take you 8 days. However, if you do a manual refresh which is 200 initially followed by 400 for the second then you can buy the pack 4 times a day for 4,600 total. You can do that safely for about 3 days until you'd run almost out of what you currently have and that'd leave you at 60 fragments with 2,200 and 20 fragments left (assuming I'm not failing with my math anywhere). Add in the 3,900 you'd be getting over the course of the 3 days if you clear all 12 trials then you'll be sitting at 6,100 which would be more than enough to pick up the last 20.

Also, we don't really know when the shops are going to update, it's all just speculation. Either way, it's your coins. If you want to rush and grab him now just for some peace of mind then I'd say more power to you.