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).

**Edit:**

Here is the schematic I used to check with LT Spice. The input signal (rect, 0V and 5V) is fed into three similar BJT inverters using the complementary BC847 and BC857 pair. The one on the left has no special tricks to speed it up, the one in the middle uses Schottky diodes for anti-saturation and the one on the right also features a high-speed bypass along each base resistor (22pF). The output of each stage has an identical load of 20pF, which is a typical value for some trace capacitance and a subsequent input.

![Schematic][1]

The traces show the input signal (yellow), the slow response of the circuit on the left (blue), the response with anti-saturation diodes (red) and the response of the circuit that also uses capacitors (green).

![Waveforms][2]

You can clearly see how the propagation delay gets less and less. The cursors are set at 50% of the input signal and at 50% of the fastest circuit's output and indicate a very small difference of 3ns only. If I find the time, I might also hack the circuit and add a real scope picture. Careful layout will definitely be necessary to achieve sub-10ns delay times in reality.

  [1]: https://i.sstatic.net/TGtEr.jpg
  [2]: https://i.sstatic.net/a4w2G.jpg