Anti-saturation diodes are connected in parallel to the C-B-diode of the transistor that is to be kept from saturation. You are doing this correctly at the npn (anode at base and cathode at collector), and it should be done exactly the same way at the pnp, just that the diode is the other way round in this transistor: cathode at base, anode at collector. With LT Spice, I get < 15 ns propagation delay times for LH and HL (no load at output, like in your circuit).

I am not really sure how you chose your base resistors. I assume you have a supply voltage of 5 V and a rectangular base drive signal (0 V, 5 V). I would suggest you use identical values for both base resistors. With 5k (5000 Ohms), it is likely that the high value of the base resistor does more harm than an anti-sat-diode would do good. Something in the range of 200...500 Ohms for each resistor seems better to me.

If you want to push the speed even further, you can try paralleling the base resistors with small (approx. 22p) capacitors. The simulation says a transition time of < 3 ns is possible at the expense of a small over- and undershoot at the output, but I would double-check on a breadboard if this can really be accomplished and if the over-/undershoot are as severe as in the simulation (spikes of 1 V in excess of the stationary output levels).