Hi Joshua,
Yes, you need to connect NST case to RF ground DURING Tesla Coil USE. (Not
Mains ground).
Your NST has the secondary high voltage windings with a center tap which is
connected to the case internally in the tar like insulation material. This
must then be grounded. One of the reasons that I know of is to save money
on the insulation voltage class of wire required. The wire on each side of
the center tap only then has half of total voltage of the output nameplate.
There are probably some other reasons also... maybe some others can chime
in on this. I am still thinking of things and debating in my head right now
on this running the coil this way and associated possible problems. But I
will say...this is not good at all to the health of the NST from what I
know. Your filter, even if working correctly, will not save it from this
ungrounded problem. Hopefully you have not started to damage the NST yet.
On your poor RF grounding, I would do what Jim said or at minimum for now
use your stubby rod and the aluminum sheet you mentioned both together.
Chris Reeland
Ladd Illinois USA
Sent from my Lenovo Tablet