The capacitors are not in the circuit to increase switching speed. They are there because someone forgot to delete them. Also, this is not a monostable circuit. Also, do not relocate the LEDs.
The circuit is intended to be a solid-state version of the original flipflop circuit invented by Eccles and Jordan in 1918. A confusion is that it has coupling capacitors that were in the original astable multivibrator circuit invented by Abraham and Bloch in 1919. Note that there is no clear evidence that one circuit was derived from the other; they might have been developed independently.
The astable circuit uses coupling capacitors, and the flipflop circuit uses coupling resistors. Your circuit has both, which indicates to me that whoever developed that schematic was not quite clear on the intended function of the components.
As others have said, you can delete the capacitors but must keep the resistors. The caps are too big for the speed-up function, and actually are large enough to (maybe) cause damage over time, by very briefly dumping too much current into the transistor bases each time the circuit toggles. On another forum I routinely disagree with a senior member about how large a capacitor it takes to cause this kind of damage over time, but in theory it is a real concern.
Note that if you move the LEDs to the transistor collectors, the holding current that keeps on one transistor is now coming through the LED that is supposed to be off. This is a small current, BUT depending on the efficacy of the LED and the gain of the transistor, you might be able to see the "off" LED glowing dimly.
And - finally - to your question: beyond a wiring error, there are several different pinouts for TO-92 transistors. The ones you are using might differ from the ones in the sim.
https://en.wikipedia.org/wiki/Flip-flop_(electronics)#Implementation
https://en.wikipedia.org/wiki/Multivibrator#Operation