What, exactly, is half of a capacitor? There's more in that formula than plate area. Anyway I can pretty confidently predict that whatever you built it's insignificant at the 50/60Hz frequencies you care about. You seem to be ignoring that discrete capacitors have two wires. Your homebrew version does too, although they may be really well disguised (like the dirt nearby). The question of where to connect your ground post is closely related to this.
Anyway, if you can, connect that ground to whatever the person that might be electrocuted is standing on. A long copper spike pounded into the ground is the favorite choice for houses and such, but probably doesn't make sense in your case. Instead, look at the specifications of the inverter. It must have something along the lines of double insulation or reinforced insulation, like the electric drill that only has two contacts on the power cord. I don't know if they'll tell you that, it may be (ought to be, IMO) a requirement for the safety standards (CE, UL, CSA, TUV, etc.) in which case they might not mention it. What does the operators/installation manual say about grounding?
I would connect it to any metal bits that someone who is trying to kill themselves may be touching and leave it at that. No, I wouldn't guess that you'll kill anybody. But then how would I know since I don't have any data about your parts and system design? OTOH, I wouldn't be the least bit surprised if you told me you got a small shock from small leakage currents.