What is the state space model for a BLDC motor
First, you probably both can and want to neglect the RL circuit.  Want, because with commutation the model gets complicated (or at least complicated to verify that it can be simplified in the manner you have done), can because in general the dynamics of the electronic portion of the loop is generally much faster than the electromechanical dynamics.  As long as the electronic part settles more than ten times faster or more than the mechanical part, you're safe to treat the electrical problem and the electromechanical problem separately.

So I'm going to just treat the electromechanical part by itself, meaning that I'm going to ignore inductance.

The first thing you need to do is to write out the differential equation.  This is your real error -- your immediate error should become apparent in the solution.  I'm going to do this just using \$k_T\$ and \$R\$, because the other constants you mention are derived from those, and I know my way works.  Note that this means you need to remember the units conversion \$\mathrm{\frac{N \cdot m}{A}}\$ = \$\mathrm{\frac{V \cdot s}{radian}}\$.  I feel it's a small price to pay.

On to the math.  Acceleration is proportional to torque, per Newtonian mechanics: $$T = J\alpha$$  Torque is generated by the motor from current: $$T_a = k_T\, i$$ (Note the total torque \$T = T_a + T_l\$ where \$T_a\$ is the armature torque and \$T_l\$ is your load torque) The motor's back-EMF is generated by rotation: $$E_a = k_T\, \omega$$ (this is why I like using \$k_T\$ throughout).  Finally, armature current is the effective voltage across the armature divided by resistance: $$i = \frac{V - E_a}{R}$$

I'm going to be bad and put that all together in one step.  Feel free to review for errors: $$J\alpha = T_l + k_T \frac{V - k_t \omega}{R}$$  Now rearrange, and substitute in \$\alpha = \dot \omega\$: $$\dot \omega = \frac{T_l}{J} + k_T \frac{V}{J\,R} - \frac{k_T^2}{J\, R}\omega$$

All of your desired behaviors should drop out of this, with the exception of the no-load current, which is a consequence of a fraction of \$T_l\$ that is always present -- you need to infer this from the datasheet (and pay attention to the fact that almost none of it is nice viscous damping that goes as \$B\omega\$ -- some is coloumbic friction that goes as \$\mathrm{sgn}(\omega)\$, some is windage that goes as \$\mathrm{sgn}(\omega)\omega^2\$, the rest is outright odd).