according to this calculator... Tire Size Calculator - tire & wheel plus sizing
...a 255/45-19 requires an 8-9.5" wheel. This would imply your 1/2" wider wheel could run a 265/45, which isn't quite an inch wider than your 245, but closer to 3/4" wider (0.787").
However, this calculator is having a problem recognizing a 265/45 and 265/40 in a 19. tirerack.com does sell a 265/40 but no 265/45's.
One thing else to consider is diameter. Those 245/45's are already pretty tall @ 27.68"...tallest OE's I've seen on Mustangs are 28", most are closer to 27".
A 265/40 is 27.34", which wouldn't be too much of a reduction in dia, front to rear. However, I think that's likely pushing the limit of that 8-1/2" wheel, plus the only all season I see at tirerack in that size is a Mich Performance winter/snow @ $357/pop.
So now you're looking at reasonably only being able to go to a 255 on that rim...which is only 0.394" wider...hardly perceptible and now pretty much negates the ability to rotate front to rear.
You'll note when playing with that calculator that not only does rim width effect tire selection, but the tires profile will also come into play. Makes sense...the taller the profile, the more rubber avail to stretch to a little wider wheel...so the 265/40 might in fact be outside the recommended width.
Unless you're able to find a 19x10 OE like wheel that's made to resemble what you have, you'll likely need to invest in a whole new set of wheels.
If you do it before you get too many miles and blemishes on them you may be able to get a little $ out of your OE's.
If you do decide to buy new wheels, you may want to consider some other concerns...for example if you want to stay with a 19". 18's are typically cheaper, both wheels and tires, but if you think you may want to upgrade your front brakes in the future, most 18's (but not all) won't clear them.