Tweaking the base resistors probably wont fix the overheating in Reset problem without introducing other issues. If you increase the series resistors and reduce the shunt (B-E) resistors to keep the transistors off when the input is floating mid-rail, depending on your desired output current, you are likely to have difficulty getting enough base drive when the input is driven to either rail.
One option would be to feed the squarewave from the PIC through a logic buffer, with a pullup or pulldown resistor on its input to set the desired output state when the I/O pin tristates.
Another option if the PIC peripheral is capable of multiple synchronous squarewave outputs and you've got a spare I/O pin the peripheral can use, would be to generate separate high side and low side drive signals from the PIC, so both transistors turn off when the I/Os tristate. This may also let you add deadtime, eliminating shoot-through, and thus improving efficiency and reducing unwanted supply transients.