Well, I agree that it is not a probable outcome, but I still think it is possible. Murat looks to be easier, but the guy was hated by almost everyone and too backstabbing for his own good. Beauharnais is far from a political genius, but he has much better dynastic connections. Also he looks like a person that could heed good advice and know his own limits.
What I would prefer to see is:
-a mid sized independent italian Kingdom centered on Lombardy, hence the Beauharnais option.
-an Austria that is more focused on Germany, leading to a more interesting German dualism.
-if possible, avoiding restoration of the Papal States, or at least reducing them as much as possible.
Maybe a slightly more realistic POD would be agreeing to one of the offers in late 1813, at the latest in January 1814, Melzi d'Eril was lobbing hard for that, but how could Eugene have betrayed his father? At that point a Napoleonic return could be even good, as Eugene could prove his good faith to the allies, in contrast to Murat probably...
As for future enemies, I wouldn't be as worried as you are, my dear Lord Kalvan: the serious ones are Austria and Piedmont yes, but I wouldn't worry much about Spain (too far), the Italian puppets (too weak), the Two Sicilies (not going to expand north very much, and they have their own instability problems), UK (no great divergence of interests) or even France (no common borders and also prone to political instability). If Eugene is recognised at Vienna he will rule as a conservative and be imho quite safe, then, when the reactionary order starts cracking in the next decades... Well let's say that ittl the Savoia won't be the only hope for unification, nor the best one.
As for the title, you are obviously right about the extent of ancient Lombardy, but I wasn't thinking of him actually donning the Iron Crown. Maybe something like Grand Duke of Transpadania could be a less ambitious and hence more palatable title?
Well, I didn't say it was impossible but rather against odds. It's true that a lot of very strange things happened in the 19th century and therefore Eugene securing a crown is certainly possible, but it would take a serious dose of luck since he was no political genius (as you say) and he has no Talleyrand at his beck and call.
In a way the major difficulties will come after his Milanese crown is confirmed, since he'll have to walk a difficult path between the conservative and the liberal camp in an European diplomatic landscape which is much less stable than IOTL.
I was alluding to this when I mentioned "far away patrons and much closer enemies": his true patrons are Alexander (whose death in the 1820s is not going to be butterflied away) and his father-in-law (whose new domains are further away, and who needs anyway to secure his new throne). I can possibly see Alexander putting pressure on Austria, but what happens when Nicholas take the throne? Is Eugene going to grant a constitution (nothing too fancy or liberal, just something patterned on the one granted by the Bourbons in France, but anyway something which will not be liked by Austria).
Mind, I'm not trying to dissuade you from exploring this what if: I'm always interested in Italian timelines, in particular the ones which can avoid a Savoy-driven unification of Italy.
I've to tell you that I don't like at all the idea of naming Eugene "Grand Duke of Transpadania": it sounds (and it is) completely fake.
First of all, starting with Napoleon's abolition of the HRE, kingly crowns were awarded with a lot of ease: why penalise poor Eugene? In the worst case, Tuscany plus Umbria might get an upgrade too.
Second, the name "Transpadania" was never used at all in history (not to mention that Romagna is anyway below the Po river
IMHO the style "king of Lombardy" is the right one (my apologies if my previous post gave you the idea that it might be too lordly, or whet the appetites of Eugene: poor Eugene will have to play the role of a shy and humble mouse for quite a number of years anyway). The only alternative might be styling him as "Grand Duke of Milan and Romagna", but it would be petty.