Although this topic is old, here I leave my opinion.
I have recently simulated almost the same 2n2222 based TTL NAND circuit, but with only one input.
The values obtained by xxxyyyba with Mulsisim are different from those obtained with my simulator.

The reverse Beta of the Spice model for the 2N2222 is 6.
The Q1 currents I have obtained for a only one +5V input are:
Ib= 0.57mA, Ie=0.70mA and Ic= 2.28mA, resulting a Br = 4.


Mod:link to old thread.
https://forum.allaboutcircuits.com/threads/bjt-ideal-maximum-reverse-beta.107376/post-822164

 

This model in Multisim is very bad. It has bad VAF and VAR parameters.
And here is how the Multisim counts the gain in reverse mode when the Emitter-Collector voltage changes.