Sorry to sound disagreeable (sp?), but I don't think a 57 would sound a whole lot different from your 58. How sure are you, though, that it's a real SM58? I don't know this for a fact, but I've read that there are a great many counterfeit SM58's in the market, sometimes sold even by reputable dealers who don't know any better. That's probably not it, but ya never know. Search "counterfeit sm58". There are things to look for on the mic to help confirm its the real deal.
How distorted is the sound you are trying to record? I sound like a broken record, because I always go here, but I've done it myself so many times, that it just always seems like a possibility when someone says they don't like their recorded guitar sound. For whatever reason (that I don't really understand), for overdriven guitar, to get it to sound the way you like recorded, it will generally need to sound cleaner than you like live. I can't count the number of times I've listened to my own playback and said "Oops, too much drive!!!!".
As for your amp... I don't know. I'm a bit of a snob about amps and that may be entirely unfair in this case, because I've never heard this amp... Lot's of good review it seems, but looking at the specs, I read "TransTube" to mean "NotTube". Like I say, that may be totally unfair, and I don't mean to sound negative, but you are trying to get a sound in your recording that your amp is first trying to "emulate" for the microphone. It's a modelling amp... Does it have a line out that you could perhaps record direct. That may actually sound better than micing it.
Assuming that the modelling is "true", the other thing I will say (that applies to tube amps anyway) is for a given distortion level, you should try to get there by turning the master volume up and keeping the gain as low as you can to get the breakup that you are looking for. In a tube amp, you want to overdrive the power tubes and output transformer to get the real deal as far as overdrive sound is concerned, rather than overdriving the preamp tubes and then just passing this overdriven sound through the power tubes as-is. If this effect is modelled in your amp, you may like the sound of recording it crazy loud. If the effect is not modelled, or not modelled accurately, well it will just be crazy loud...
Maybe someone with experience wth that particular amp will comment. I'm sure it can make good recordings. Often times it's just a matter of finding the sweet spot whatever the gear.
Good luck,
J