Coriolis tells me that a Phantom with vanilla MGC armor has integrity of 630.
G1 HD increases that to 706 or 762 with DP.
G5 HD is 832 and is 898 with DP.
For comparison, a single 5D HRP will give you an extra 390 integrity, moving up to an extra 738 with G5 HD + DP.
In a nutshell, it seems like you've got a LOT of scope for improvement on what you currently have.
Thing is, the Kraits aren't exactly terrific fighty ships.
The sort of mod's you need to do to the Phantom will make it okay but a similarly modded Python would be significantly better.
Did you post up a build of your ship as it currently is?
If not, people will be able to provide more specific advice if you do.
Personally, I'd always try to improve the shield before accepting that it's going to get broken and then taking damage while trying to get the kill.
Lastly, if you're really struggling in CZs, or you're struggling to obtain mat's to complete upgrades, I'm currently on my way back from Colonia and should be back in the bubble by tomorrow.
If you want to hook up and go blow some stuff up, either for practice or for mat's, shoot me a PM and we can work something out.