Note that you have maximum Miller effect in this configuration, which makes the large rectifier 1N5817 rather undesirable. A signal diode like BAT85 or BAT54 would be more suitable.
A PN diode can also be used, in which case you need to place it on a tap higher up the base divider:
You can use this method to set an arbitrary Vce(sat) value, useful for low-accuracy clamping applications.
Alternately, a PN diode is fine with a Darlington transistor,
But there is a caveat: the real circuit will oscillate. The left circuit simulates as stable, but the real circuit oscillates. The right circuit has been modified to reproduce the real oscillation. Unfortunately, the parasitics don't happen to be physically realistic: the load resistor R1 is a wirewound with about 50 times lower inductance than shown here, for example.
Probably the root cause of this discrepancy is, a real transistor has some delay, or higher order poles, whereas SPICE has no concept of delay*, and has a single-order model (lumped terminal capacitances, current gain goes to unity at fT).
*Except when transmission lines are explicitly used. (Built-in components like transistors do not use them.)
Anyway, for faster switching, you need to discharge the B-E junction. BJTs are voltage-controlled, not current. Instead of an open-collector driver (active pull-down, Q2), have an active pull-up phase as well. Then you can use the speed-up cap across the series resistor to do the business.
Also, consider MOSFETs. These have lower gain (= needs more drive voltage), but that's not such a big deal (e.g., use a bootstrap gate driver IC), and you don't have stored charge or Vce(sat) to worry about.
Finally, as for the general circuit and apparent purpose -- I don't see any way to control or limit current here, nor will the currents or voltages be balanced in any obvious way, with the values shown. The canonical way to build a balancer circuit is to use a dedicated regulator IC for each cell, sending excess charge current back into a common rail. Each regulator controls its own inductor current and cell voltage independently, giving maximum benefit, without much added cost (regulators are cheap, exploding cells are not).
Tim