In the CSN you will read that Tesla tested with the return circuit being tuned to the same frequency as the secondary and extra coil. In other separate notes you will read that the return circuit can be any frequency.
To achieve CW you will most likely resort to transistors.  Transistors put a limit on you primary circuit voltage and consequently on the output voltage as you already noted. The voltage required for this system to work is much higher than what can readily be achieved with transistors.
I also suspect that the abruptness of a spark gap plays a role and there is really no transistor that comes anywhere near what a spark gap does in that respect.
I have built a transistor driven 50W TMT, more or less as you describe it and did not get any interesting results.