Agreed. It is pretty hard with discrete analog devices. The gain of transistors can vary by as much as 3 to 1, so you end up making it and adjusting it just to make it work.
The "gain" specified in dB is actually a fractional
voltage gain due to the different input and output impedances. If someone wants a voltage gain of 16 they should just say so, not try to dress it up with dB figures.
The gain of the first stage is approximately RC / RE and the input
impedance is approximately hfe * RE. But the bias resistors appear in parallel with the inputs and the loads for both stages.
Both of these calculations force very large values of RC and RE so the collector current becomes very small and the base current gets microscopic.
If I had to use those components, it might be worth using the FET as the input device.