What I have taken to doing is cycling through my different pets, sometimes at the end of a month, or more usually after a particular season has ended or a holiday has come and gone. This way I send out all my pets at one time or another and I don't get overwhelmed trying to craft enough pet feed for them. Usually I stick to having only 8 out at once, though I've had 10 out for the past couple of months because of needing (and hoping to receive from them) expansion items like wood planks, and shovels and pick axes. I've also noticed that having too many pets wandering around or jumping up and down seems to slow down my device, but 8 seems to keep gameplay smooth.
Perhaps exchanging pets in and out (after collecting from them but before feeding them again) would be an alternative to expanding the habitat capacity?