I've built a number of single tube ECO oscillator/transmitters. In each case, I have also plate modulated them with an external modulator. I also helped a friend design one using a 6146, that he operates on 75m AM with an external plate modulator.
Bottom line:
I agree that these transmitters are very tough on crystals. Unless you use larger vintage FT-243 crystals, you will likely have problems with heating / overheating, and large amounts of frequency drift on key down. [My friend only operates on 3835, so he needs only one crystal that works okay in his 6146 ECO]
Unless your principal objective is to build that particular single tube / ECO transmitter, I agree with the advice in the other posts:
Build a transmitter with a separate 6CL6 (or 6AG7 octal tube equivalent) crystal oscillator, with regulated screen voltage ... following the design details given on Dr. Greg Latta's amateur radio web pages.
http://faculty.frostburg.edu/phys/latta/ee/6cl6xmtr/6cl6xmtr.htmlIf you want to operate on 7MHz or higher frequencies, you will need a tuned circuit at the output of the oscillator... coupled to the grid of the 813 with a 47pF capacitor. You need this because the input impedance ( grid-to- cathode) of the 813 is too low, at 7MHz and above, to produce a large enough 813 grid drive voltage swing, given the plate current swing of the oscillator.
Stu