I'm gonna go against the grain and say...maybe try a very nice, clean real guitar amp. Finding a vintage one might be pretty spendy, but you might get lucky if you search a bit and are patient. Alternatively, there are some EXCELLENT amp builders you might look into for newer gear. Milkman and Morgan are two that come to mind immediately and there are plenty more. PRS is making John's new amp and it's stupid expensive, but they have other excellent amps too. Again, there are plenty more to choose from. Honestly, you could do a damned good job with a decent newer Fender Deluxe, Deville, Twin, etc. You don't have to go crazy but let's face it, the sexier the amp, the better you'll feel about it.
The Axe FX is insanely good at what it's designed for...which is NOT "amp in the room" as far as I know. It can do that pretty damn well, but it takes a bit of work and outboard gear and an acceptance that you're taking the Axe a bit out of its element. I was running my II XL+ through a Matrix power amp and into a Mesa 2x12 cab. It sounded great. Then I plugged into a Blues Jr. just to test it prior to a sale and remembered just how great a real amp can sound in the room. Sold that Blues Jr. I have a Mesa TC-50 and a Mesa Mark 5:25. There's *something* about having the amp in the room that's just different. It's very subjective and difficult to articulate, but some find that difference "better", some find it just different and not necessarily better. I guess that's part of the reason the FX8 exists. It caters better (easier) to the "I want the amp in the room" crowd.
Something exceptionally important that I think gets overlooked/underestimated is the organic simplicity of a tube amp. You can sit down, turn it on, twist a couple of knobs and be happy as a clam. With modelers and such we almost invariably end up scrolling through menus, making selections, tweaking those selections, scrolling through more menus, making more selections and tweaking those, etc. For some people that's definitely a part of the process and they love it. For others all that is just a means to an end...the end being that feel of sitting in front of a real amp. By the time those people get that feeling (if they ever do) the joy of the moment and the inspiration may have vanished.
Go listen to some of John Mayer's CD's (or someone else's) in as high quality as you can. That's the type of thing the Axe is built for. Go to a concert (side note: I'm going to see Mayer on Aug 1 and Metallica on Aug 4). You ain't really hearing the sound of the amps "in the room" in Mayer's case. You're hearing them mic'd up, running through a mixing desk, and through a huge PA system (and a bunch of other stuff). In Metallica's case these days, you'll be hearing the Axe FX's running through "some stuff" and eventually out to the PA system. All that does sound fantastic, but it's NOT the sound you get when you're standing in your bedroom in front of a decently cranked amp. That's a whole other experience. Again, the Axe FX can get you there, more or less, but...
If you really want the sound of a great amp in the room, and if you're the kind of person for whom that simplicity is valuable.... Get a great amp and put it in the damned room.
Oh, and was stated earlier, don't expect to sound like John Mayer or any other player. Expect to sound like YOU playing through a great amp.