IMHO I think having limited number of days or anything less than 5 starting days might be too little time to breed/buy and train, most of all to lvl 7+
You can just save the higher level ones until those 7 ones come out. And does it really matter, it's not like missing out on a handful of the requests will make you lose the game. This game is super easy in terms of reaching the goals you need. The monthly payments are only 500. The only other costs you need is buying more monsters, and some events for romancing. I found no issue whatsoever in terms of needing money.
I let a number of them pass/expire, I just made the first payment. 2 days later there are no new posts/requests for monsters. Maybe having alternative means to earn money could be available? We do have .... Cow Girls so maybe milking them (50 per cow) and I understand there are plant girls too, maybe harvest fruit from them?