But the lower right most transistor, switches on, well before the lower left hand one. To make matters worse, while the top transistor is conducting, the lower pair of transistors, ALSO begin to conduct, potentially causing lots of current to flow. (500KHz = 1,000,000 voltage transitions per second). The simulator seems to say this is about a microsecond, which for a signal which changes state about every microsecond, it is too slow to keep up. So not much current available, to fight the stray and base capacitance's. So we have about 700 milli-volts on the bottom pair of transistor bases, so there is only a few hundred milli volts across the 1K resistors. There is some current in the pair of 1K resistors (while it is transitioning, and the bottom pair of transistors are trying to switch off), so the relatively weak port pin has a few hundred (very approximately) milli-volts on it.
When the PIC's output port pin (input on diagram), attempts to switch off. Since it is NOT my project, I DON'T want to build it for the OP, sorry! I've had a quick look (so could easily be mistaken), at what is going wrong. At 250KHz, it does work, but takes ages to switch states. At 500KHz, it basically does not seem to work. I've tried simulating it (LTSPICE IV), with general purpose parts, but it does not seem to work very well. But in practice, it can be exceedingly difficult to design it, given the huge potential of shoot through and/or the wrong voltages being produced at the output. The pair of bipolar transistors, was a good idea in principle.
Sometimes the most successful solutions, are found, immediately after something does not work quite right. Your low gate capacitance fets idea (driving the bigger output fet), could we worth trying. Are so powerful, you don't even need the output fet, unless the currents are somewhat big, or it needs to dissipate power. But some fet drivers I bought a significant stock of a while ago. I prefer to take the quick/lazy/easy option of using standard fet drivers or fets with built in drivers (expensive, but ok for one offs).
For one offs (with little prospect of manufacture), or early prototyping. The best ideas (low cost), seemed to be to use cheap, high speed logic gates, and parallel the outputs (not everyone likes doing that), to increase the output drive current capabilities, still further. Ironically I was looking into a similar problem, fairly recently. Hundreds of KHz, is a completely different matter, especially if you want high conversion efficiency and/or low device dissipation. 2 KHz is normally very easy with MCU port pins (unless very high currents or something are needed, even then you may still be ok). I did not realize you needed somewhat high frequencies.
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