Update: I just now realized the classes have to be completed rather than started, making it sixth grade until I can actually repurchase them (if things stay the way they are at the moment). That'll be at least mid of August 2018 for my character. You cannot be serious about this.

You're both completely right. I didn't even think about that. How about the requirement is having 600 galleons in Gringotts? At least for the first time. 
Therefore you couldn't transfer the first 500 galleons from a second/third/forth/... account to your main account and it also isn't enough to quickly solve Peeves' and the Weasley twins' riddles. It'd ensure you'd at least spend a few days on your account, since you also can't start correcting homework right away. 

Also it doesn't make much sense that some of the pets require year 5 class of CoMC. For example an owl that is described as fitting families with yound children. I had one, now I don't since my character is in third grade. It just doesn't make sense to have a requirement that high with a description of the animal like that.

I'm totally with Ace on this. I'm unable to buy back any of my pets as they require 5th grade, meanwhile my character being a thirdgrader. She got both of her pets as gifts. What am I supposed to do? Pretend they ran/flew away? Pretend they never existed in the first place? Or break the rules and pretend they still exist until I can actually repurchase them in about 15 weeks? 

My character is in third grade at the moment. She got both of her pets as presents. A cat from her head of house during her first year and an owl from her best friend for christmas this school year. Which is just about two weeks ago. Now I am not able to buy either of the pets for her as they both require the fifth year class of Care of Magical Creatures. This means it'll be another 15 weeks or so until she's there. It's quite frustrating.