8K would be dandy for the 5842, use a 50.6 Ohm resistor for R1 on your C4S and an HLMP-6000 under the cathode. The 8K vs. 5K load is going to reduce the available output a bit, but at the same time you'd have potential for lower distortion and a lower noise floor.
With the 5842, I'd use four 1K grid stoppers, 1 going to each pin available on the socket for the grid connection.
Do also note that using an MJE5731A in place of the MJE350 is a nice idea, and the note for a heatsink.
A string of 0D3's is a good idea (also suggested in the article), but if you are limited to 18mA, that won't make much sense. A PT-7 power transformer would accommodate such a circuit nicely.
-PB