A LC circuit needs power to flow back and forth between the L and C in order to have it resonate. The diodes let power flow into the inductor but the inductor is not able to send the power back trough the diodes into the capacitor. If you see a way to send power back trough the bridge then please explain how.
And again you're wrong. I don't see how you don't see the obvious. Current flows just like it would without the rectifier. Now i'll draw it for you.

Yes, notice how the positive side of the capacitor always ends up on the top end of the inductor. This puts energy into the inductor.
In order for the inductor to give its energy back out the voltage across its terminals has to go negative. It will indeed do this on its own if the capacitor stops supplying voltage. You can imagine this as replacing the inductor with an imaginary battery where the positive terminal points down.
If you track the flow of current around you will find that the current splits up on the two diodes and continues flowing trough the other two diodes and gets around to the inductor again. This makes for about -1.4V across the inductor due to the diode voltage drops. So the inductor is giving off energy but all the energy its giving off is just turning to heat on the diodes rather than making its way to the capacitor.
If you don't believe me try simulating this circuit in SPICE or if you don't trust simulations then try building and and see for your self that this can't resonate in any usable away.
Yes indeed ZVS induction heaters work really well at high frequency. But notice that the coils they use have small cross sections and only a few turns? This is to keep inductance low so it can resonate so high while maintaining a very large current at voltages that MOSFET transistors can handle. The small coil has much less energy storage capability so a lot less power is needed to build and destroy the field around it.
All you need to do is to drastically reduce the number of turns to get to a coil design similar to a induction heater and then it will operate at high frequency without involving the massive power levels.
I know resonant frequency formula and i clearly said i will have to lower the number of turns/inductance to increase the frequency which is expected to be ~1.44KHz with noted LC values.
Yes but this reduces the strength of the magnetic field generated in the coil.
Im under the assumption that your goal is to generate a magnetic field in the coil of a given strength (8A into 600 turns requirement). So if you half the number of turns to 300 then a current of 16A is needed to produce the same strength of field. Halving it again to 150 brings the current to 32A etc... By the time you end up at 10 turns the current is that 480A from before.
The other way is instead of a 600 turn coil you make two 300 turn coils each carrying 8A. By the time you get to 10 turns per coil you need 60 of these 8A each stacked together to get the same field.
Either way the reduction in the number of turns just shifts the high voltage requirement into a high current requirement. The power requirement stays the same 350kW because you are generating a field of the same size and strength.
I don't want to start off a free energy discussion because of how such discussions usually end up.
Zero wish to discuss it, you are not ready for FE and that's ok. Some day you will realize how undescribably wrong you were.
Not that i'm not ready for it, id love to build myself a free energy generator to power my stuff. But so far i have yet to see blueprints for a free energy device that people managed to reproducably build and make it work as claimed.
To top it off a lot of the content on the topic of free energy has inconsistencies in the theory of operation or badly set up experiments. Things like misinterpreting magnetic forces, ignoring negative/positive signs on numbers, showing a misunderstanding of phase in AC power, doing measurements in crude or incomplete ways etc. All of this did give me a bit of a negative bias overall to this type of content.