Can I feed this new transformer/subpanel off two 120vac legs of the 480vac panel?
A 25kw EV charger is enormous.  It's not a residential-grade unit.  It is aimed at commercial outfits, and most of them will expect to put a 25KVA load on 480 volt 3-phase.  This is for at least three reasons:


they want to evenly load all three phases, so their power bill isn't wacky.  
they will not want to provision a 30KVA transformer for each charger.  Keep in mind a place fitting a 25kva charger is likely to be fitting several.  
They want to put three 10AWG wires in a 1/2" conduit and call it done, not wrestle 1/0 Al into 1-1/2" conduit. 


The upshot is this: the manufacturer of this unit will certainly, also, make this same unit in 480V 3-phase.  And may even be able to sell you a kit, or simply instructions, to jumper the unit for 480.  Or you could sell this unit to the plentiful supply of people who have 240, and buy a comparable 480 charger.  Putting in a 30KVA transformer is just crazy. 

And while we're on that subject...

480V is not for touching.

Your skill-set is way-deadly-not-nearly enough to even be opening the door on a 480 panel. That stuff is different by nature and much more deadly than 120.  You lack key concepts of how 480V power works.  You only just now discovered that you can't take 240 off 480 the way you can take 120 off 240. Those figures are "not even wrong".  It seems like you have little bits of  knowledge, like that gained on the way to a singular goal but without comprehension.  Sorry, nothing personal but you are way out of your depth here.

Rarely do I say this, but hire a professional. 

What's more, since you are not in a single-family home, doing so is mandatory anyway.  A company or landlord must hire professionals unless it retains an electrician on staff.  You'll need to pull a permit anyway, and they will want to know who the electrician is.