Considering the power dissipation of a transistor
It doesn't look feasible without some sort of improved cooling beyond just a bare transistor, looking at the average power alone. I don't have hard numbers on how short is short enough for peak power dissipation, but half-millisecond pulses seem sufficiently short relative to the thermal time constant of the device.

Let's take a look at the datasheets for the 2n2907:



and the 2n2222 (I wasn't able to find a 2n222 so assumed it was this particular typo):


Let's assume that the average power is 1 W for each BJT, ignoring peak power at the current moment. Assuming the transistors are in room-temperature air, the TA (ambient temperature) value controls the maximum rating, meaning that you can only dissipate 400 mW/625 mW on the two transistors before failure may occur.

While the TC values look promising (as they both exceed 1 W), they assume that you can somehow keep the transistor case cooled to 25 deg. C. This is going to be pretty hard, and you're going to run into your derating curves soon enough. 

Let's continue assuming that ambient conditions are 25 deg. C still air. Following the T_C dissipation rule, we find that the total device dissipation derates to 1 W at \$25\,\text{C}\ + \frac{500\,\text{mW}}{12\,\text{mW/C}}\$, or about 65 degrees centrigrade (this is 40 degrees above ambient).

We thus need to dissipate a watt of thermal energy from the transistor body, while operating at a case temperature of no more than 40 degrees above ambient, for a thermal resistance of 40 deg. C per watt. According to some of the data in this answer, a good heatsink will barely pull that off, considering every assumption we've already made so far. If the device is enclosed in a case, or ambient temperatures are higher, bets are already off.

See if you can use a larger transistor with a suitable heatsink, such as a TO220 or even a TO3 (which might be overkill), to get some more margin over your operating conditions. Alternatively, if you have a PCB with a good ground plane or copper pour, see if you can use an SMT device with a large thermally-dissipating tab (such as a DPAK device) to improve conductivity down to your PCB.