I shouldn't post this yet; there's surely some catch that will prevent you from going this fast. But, I'm doing it anyway. One of my favorite NPN/PNP pairs are the MPSH10 / MPSH81 RF transistors. Obsolete in TO92 now (although I have a thousand or so kicking around), they're still available in SOT23 as MMBTH10 / MMBTH81. With an ft of 600+ MHz, this pair is twice as fast as my other "fast" favorites, the 2N3904/2N3906 (300 MHz ft). Anyway, I couldn't help but simulate some CBJT inverters with the RF pair. Here's the input to, and output from a chain of 10 inverters. One edge is delayed by 3.6ns, the other by 5.0 ns. That equates to a propagation delay of under 500ps per inverter. Pretty fast.
Here's the circuit. It might be difficult to find in the parameters, but the input resistor is 5.1k, the speedup capacitor 47p, and the feedback resistor 15k. The power supply is 1.2V.
If you want to play around in LTspice with this, I've uploaded the simulation file. I haven't even simulated a 2-input gate yet, so that may or may not work. I also haven't built one of these yet. Even testing it may provide some unique challenges.
I am still working on choosing the R's and C's to optimize the 2N3904/2N3906 pair. I started with a 1k input resistor because I have a giant reel of them from a late-night ebay purchase years ago. This is perhaps not the best objective function for optimizing the design :-) So, I'm having a close look at the R's and C's, considering speed, power, fan-out, etc, and then testing on hardware to make sure the simulations didn't lie. It's going to take a little while longer.
I ran a 5-inverter ring oscillator simulation with these transistors. This makes it look like actual propagation delays are closer to 1 ns. I still have no idea if these speeds will be achievable in reality.