Consider the open drain port-pin driver's view ...

If there's, say 11 kOhms to +5 and 22 kOhms to gnd, then there'd be quite nearly 3V3 at the port pin when it's at '1', and, of course, the port would have no trouble pulling the 11 kOhms down to gnd when it's at '0', since the 22 kOhms would help with that.

I don't have my spec's here, since I'm in the midst of moving, but ... I doubt it would be difficult to find a pMOSFET with a gate capacitance considerably less than what you have found so far, but as I mentioned previously, this can impact turn-on time. I think the '340 can drive a divider an order of magnitude lower than what I mentioned above ... perhaps more, but that choice is up to the designer. After all, the pMOSFET should be chosen to meet relay coil current requirements. The relay characteristics will be the rate-determining step, rather than the transistor's switching time. I doubt a big transistor is necessary, so, being small, the channel area will be small, hence the gate capacitance will be lower than on a "big" pMOSFET.

If the problem is too difficult, then there are, after all "high-side switches" that can be driven with 3V3 logic that contain the MOSFET and provide the necessary control for it. Some of these are VERY small and not terribly costly. They save lots of critical design effort.

RE