How to combine multiple transistor logic gates without gigantic voltage-drop?
I actually did this at school back in the 60's (yes I am that old). We used them to build a small and simple 'computer' capable of addition, subtraction, multiplication and division.   

The problem you have is that the gate circuit's inputs and output voltages you are using aren't really compatible. You would find it difficult to expand the number of inputs on a gate beyond two and its quite likely that the 'high' output of one gate isn't quite 'high' enough for the input of another. 

What we did back then was to base everything on a simple inverter circuit (or 1 input NOR gate) and build from that. 

The advantage of this approach is that you can increase the number of inputs to the gate by adding another resistor. Any input over 0.6V will operate the gate. I've shown resistor values of 10K and 4k7 (to match your circuit) but unlike your previous circuits the values here can be altered quite considerably. e.g input 470K, output 47k and it still works fine.

I've drawn out some of the basic gates - NOT, NOR, AND, NOR, NAND. Following what I have drawn I'm certain that you can produce any other gate you require. 



You might also find these circuits useful


And a divide by 2 (counter)