How about this. Up until the Ausgleich Transylvania was ruled directly by Austria via a military governor and there was no love lost between the Hungarians and Romanians who actually fought against the Hungarians during their uprising in 1848. Perhaps during the Congress of Paris as a neutral observer Austria could suggest rather than having the Danubian Principalities of Moldavia and Wallachia become quasi-independent self-governing principalities that they instead be joined with Transylvania under a cadet branch of the Habsburg family as the Kingdom of Romania?
The main problem with this is that Max has just destroyed his chance of reconciling with the Hungarians. They see Transylvania as an inseparable part of the Kingdom of Hungary. Uniting it with Hungary proper under a single administration was one of their main goals. And it has a large Hungarian Szekely population at its eastern edge which would be at the heart of this new Romania. So it would become a source of anti-Habsburg sentiment and Hungarian irredentism and we saw how well that played out post WWI.
Other than that I like the idea, maybe they just give up Bukovina and force the Ottomans to cede northern Dobruja to secure the 'neutrality and open passage of the Danube' or something like that. So basically a slightly larger version of OTL pre WWI Romania as a buffer between Russia and the Ottomans. I think Max would have to follow up pretty quickly with plans for Hungary and Croatia because setting the precedent of a Romanian Nation-State without quickly addressing simmering nationalism within Austria is a recipe for disaster.
This started me think on what Archdukes are around at this point-at least compared to the plethora of Archdukes one encounters by the end of the century. There's actually not all that many that would be suitable.
Of Max's two brothers only Karl Ludwig is suitable, in '53 he's unmarried. But Max is too and has no heir so Karl Ludwig is his heir. So putting his brother on foreign thrones is a bad idea.
The Duke of Teschen has three surviving sons, only one is married. One will succeed as Duke of Teschen so that leaves two.
Joseph Palatine of Hungary has two sons, neither is married. One will succeed his father as Count Palatine of Hungary so that leaves one.
Archduke Johann has already contracted a Morganatic marriage so he's probably going to be passed over.
Archduke Ranier Joseph has five sons but they're all under 30. And he's already proven to be an inflexible conservative as demonstrated by his disastrous stint as Viceroy of Italy. And there was no love lost between his family and Maximilian so again likely to be passed over.
So I count three serious candidates, not that many given the size of the family.