I understand that the treble dispersion isn't that great. I think some may refer to it as not detailed.
Is there a tweeter available that takes the 360 to the next level in that area?
The cross overs are at 350 Hz and 3.3 kHz. That means that that little 3/4" tweeter is doing everything from 3.3 kHz all the way up to 20 kHz?

That little fella is gonna need some help.
Edit: I have an undetermined amount of time off work and am playing around with them. So far I have one of them gutted to Super Glue the magnetic shields to the baskets. I'm taking baby steps in the modification process. This is step one.
Actually the treble dispersion is great. The only defect with the tweeter is that the break up mode is 21KHz and if you had excellent hearing, the associated effects just get into the audio range, if you still have very accurate HF hearing. Most people will not hear this.
The thing I a do notice, the impedance curve shows that in the bass these speakers are not only below four ohms, but current and voltage are out of phase by 45 degrees where impedance is lowest. These things are going to run all but the highest current amps out of gas. If the amp runs out of gas, and almost all receivers will, then the roughness will be noticed in the HF and the tweeter get the blame.
Another thing, as so often in three ways, the polarity of the woofers is reversed in relation to the mid and tweeter, in order to get a satisfactory transition between woofers and mid. Now I'm guessing the speakers are wired to put the woofers to move forward if a battery is connected positive to positive, negative to negative to the speaker. You might want to try this.
Now if you combine this with a center channel speaker, that does not require any reverse polarity at crossover, then the mids and HF are out of phase and there is nothing you can do about it.
Now a crossover at 3.3 KHz is pretty high, there is little power above that point.
You can not swap one driver for another in a design, the crossover has to be designed to a drivers acoustic roll off and they are all different.
The waterfall plot of your speakers is very decent, for speakers in that price range, until the 20 KHz point. I would leave them alone.
Those speakers will give an auto set up fits, in fact I would not use one. There will be severe blending problems with a center speaker because of the reverse polarity of the woofers from mid and HF drivers.