I was present when the online brazilian monarchist movement started...
Of course it has changed a lot since then and I'll avoid making a rant of how much I hate it now to not enter in modern politics, rather I'll talk about how it was when my old buddies were still the first few of them in order to help you with your question:
The main thing they had going was not that monarchism = empire's back, problems solved
It was that the brazilian monarchy had a reserve power known as "poder moderador", Moderator Power in english, that allowed the would-be-figurehead monarch to fire the parliament, senate or the deputy chamber in cases of severe mismanagement or corruption that would allow whoever who sits on the throne to (temporarily)stop the governamental corruption that plagues modern Brazil and prevents it from reaching it's true potential
Of course there's problems with this narrative:
-First a monarch is not necessarily needed to bring back the "Moderator Power", which is one of the main reasons why I'm not a monarchist, but the main argument of the monarchists(that I agree with) is that any elected president in a parliamentary republic who had this reserve power would use it to benefit their party or refrain from using it to not damage said party. And yeah a monarch is not necessarily neutral or looking for the nation's best interest, but not being part of a party is a positive thing on itself
-Second is that the Emperor's power in Imperial Brazil was waaay less restricted than monarchists believe it to be, they want a figurehead with no executive power like Queen Liz with this reserve power as a emergential prerrogative. Problem is? Pedro II could use the Moderator Power whenever he wanted, sure he didnt abuse it but he hell sure could and besides that he could also point ministers left & right, sign or veto laws and all that kind of stuff
In short, if you want the "brazilian monarchist dream" to be real(with some realism of course, we certainly arent going to beat the British Empire here) you dont necessarily need Pedro II to stay in power, the old monarchy to survive or for us to be a superpower
What you need is:
A) Butterfly away the military dictatorships in order for Brazil to have a ininterrupt democratic tradition, since that was what made the early republics so traumatic
B) A system with a figurehead that doesnt belong to any political party
C) Said figurehead to be able to call for new elections and fire the government under emergencies(such as Mensalão, the Lava Jato operation and the Covid pandemic) but not arbitrarily
In short, make brazilian politics as good as Norway's and Brazil a developed first world country
Could be done? I dunno, maybe its ASB, I think it's possible tho
Either way I hope that helps with your scenario
If I broke any rules here in regard to not bringing up politics I apologise in advance to the admins