I'm not aware of a way to remap the scroll wheel within Minecraft, so I think your best bet is to look for third-party tools that will remap your mouse keys for you. After a quick Google search, I found X-Mouse Button Control for Windows, and USB Overdrive for Mac.
Looking at screenshots of both programs, they both allow you to remap mouse buttons as mouse wheel up {MWUP} and mouse wheel down {MWDN}, which is perfect for item-switching in Minecraft.
X-Mouse:
USB Overdrive:
Tracking technology
Laser mice are generally the best, though their extreme precision occasionally causes problems with awkward surfaces. But I play on a rough wooden table with my laser mouse and I rarely notice when I'm moving over the wood instead of my mousepad. Optical doesn't work well with reflective or black surfaces. I'm not really sure what the complaint about laser is about honestly. I am currently unable to find a surface this cheapo laser mouse can't work perfectly on.
DPI
The best thing you can do is have a DPI switching mouse. This has two benefits; the first is letting you immediately switch the mouse movement speed (go from instant-turning speed to super precise sniping movements) and the second is letting you find exactly how sensitive you're comfortable with the mouse being for a given application or surface. Since I'm used to my high-DPI mouse I don't really switch it down (or all the way up) that often, but it's a nice feature to have.
If you want high DPI (I recommend it) again, laser is best; they're usually double optical or more. My Logitech G500 is ridiculously sensitive at 5700 max DPI, but right around 2000 feels nice. Remember if your mouse is too sensitive you can lower the pointer speed via software.
Ergonomics
For ergonomic factors, get a "handed" mouse if at all possible. If you're Left Handed you might go with an ambidextrous mouse (or if your partner is differently-handed and will use it as much as you do), but generally a "handed" mouse is far more comfortable to grip.
Size
Depending on your grip, get a mouse big/small enough for you. My hands are large so I have to scrunch up my hands (claw grip) or let my palm all off the mouse (fingertip grip). To palm-grip the mouse I need a mouse with a big "butt". Razer has a good guide to grip styles if you're confused by these terms or want more info on grip styles.
Weight
Weight-adjustable mice are also nice. High-DPI, low weight mice can be a pain to use; I prefer them a bit heavier, but the best thing you can do is manually adjust the weight. This sounds silly to some but adjustable weights are pretty common in mid to high end gaming mice.
Wireless
I've had issues with Bluetooth but what really matters is interference; the more wireless devices you have the more likely there's some interference going on. I've had issue with bluetooth and non-bluetooth devices.
Battery really shouldn't be a concern here; your mouse should last weeks between charges no matter what. General battery specs should be listed by the mouse anyway, so there's no need to consider which tech is going to eat more battery.
Multi-axis/multi-touch mice
For "two axis" wheels, if you mean Apple's multi-touch mince, those are terrible for gaming. Physical buttons are a must for one thing. If you mean horizontal scroll "tilt" wheels they usually don't get in the way of gaming, just make sure it's not too sensitive. My Logitec G500 requires a bit of force to press the horiz scroll which is good, an older Microsoft wireless mouse was sensitive enough I often accidentally pressed the horizontal scroll buttons while moving the wheel.
Best Answer
As you already mentioned yourself, this is most likely a ghosting problem. Not quite ghosting, but rather jamming. But these are both rollover problems
"Gaming" mice often register themselves as additional keyboard device to your operating system and they can suffer from the same problems. Either your hardware can't handle the combination of certain keys, or the driver on your computer is not fit to recegnize given combination. (some source here)
It seems like your mouse is of medium quality and does not provide proper key rollover for the thumb buttons. I dont't think there is much you can do besides ensuring that your driver is up to date.