Hellfire of Demises cannot be done indefinitely, though, and Fireballs aren't enough to stop it unless it's in the much earlier phase, and he needs to spend this time recovering so he can take it out all at once. If you didn't notice, it accelerates every cycle it gets rebooted, going very quickly to begin with but has become even faster at regenerating, too.
Negatives are important to consider because of how many Hellfires of Demises and other forbidden-tier spells he can cast of that level before his mana goes into the negatives, and then how many from that before he goes further. He's treating it as a True Dragon fight, not just paltry curse removal. The slimes reading up on the hidden room is to check for any useful secondary information, not to find some key to defeating it for good or anything; he just needs apply more cowbell, and for that, he needs to conserve and replenish mana.
I don't understand what you mean by spending time recovering. From fireballs? No, that's infinitely spammable. And I'm not suggesting anything stronger.
As you yourself said, fireballs are perfectly fine for mopping up the curse at it's earlier stages, so that could be done forever. And if he did it smart, like I suggested, and used the 16x boosted ones which aren't any more expensive and are as strong as Hellfire of Annihilation that could kill off the 9 dragons stage just fine, it wouldn't even need to be cast that often. Mana regen would be virtually unimpeded, leaving space for trying out other magic no problem.
And no I didn't notice any acceleration, where are you even seeing it? Yuuji didn't notice anything like that on the initial restart before fighting the lab members, then while he fought them for a while it slowly reached the 9 dragons stage and after restarting the process again it took two whole statements about time passing and a fade to black time skip to get back to the 9 dragons stage again. Didn't look any faster at all, and if anything, the second restart was slower, since the first creatures to be spawned were smaller and weaker.
The point about conserving mana for big spells is moot, since my whole idea is about conserving and even recovering it, I never once suggested anything that would drain it. And it is just curse removal as long as he stalls the curse's progression and doesn't let it evolve, which from the look of things could be done indefinitely.