Sorry I sound so depressing, but the more I looked at it, the more 
trouble I realized. I've been down your road with a small coil a while 
back. It sucked! I had a couple hundred more turns than yours, but the 
coil was even smaller. Primary was fixed at 4 turns and I tried it 
with a 7.5kV 20mA NST. I eventually installed a 12/30 to force some 
power into the coil, but it was still dismal. I ended up giving it to 
a buddy. He thought if he wound another layer of turns on the 
secondary he could get it working better. Too bad he didn't ask me 
first. Oh well.
If you want a good performing coil, then you need to design with the 
following in mind:
1) 900 to 1300 turns.
2) H/D ratio between 4 and 5.
3) A coil diameter of 4" or larger.
3) Good static gap with lots of air cooling or srsg.
4) A transformer about 12kV or near with at least 60mA.
5) An MMC cap designed for LTR operation (it's value) for the static 
gap or srsg (and those values are different).
6) A primary that tunes between 10 and 15 turns.
7) A toroid sized appropriately for breakout, loading size, and as 
smooth as you can get it.
The above are just some very basic preferences. Your coil hits #2 and 
slightly #3.
I'm sure if you worked with the coil, that you can get it performing 
better, but there is a limit with the coil and that's what I'm trying 
to get across. I guess if it were me trying to get the coil working 
better, I would ditch the bottle caps and build an MMC with a larger 
cap size. But this would require a larger turn primary, so I would 
have to build that also. I would also upgrade the NST and install a 
toroid top load which will help lower the frequency (which helps in 
other areas).
It of course takes work, time, and money to make a decent coil. It's 
not rocket science but there are pit falls to watch out for and 
experience is the best teacher.
Take care,
Bart