Class D ceases to be very meaningful up at those frequencies. Much of the time is spent slewing the gate and drain voltages, so that little time can be said to be spent purely in a saturated or cutoff condition.
Gate driver ICs have been seen, from time to time; IXYS RF used to have some beefy parts, with wide flat leads capable of actually driving that much power. They were even more expensive, and poorly stocked if at all. I haven't checked since they were acquired; I assume they're long since discontinued.
The standard RF approach is to just blast it with something rough, probably not very sinusoidal nor square, using another amplifier, which itself may be tuned or baseband, single-ended or push-pull (and at that, push-pull or totem-pole). A coupling network may be necessary, say to transform a 30V output swing to the ~5V gate swing needed.
Several watts of gate drive is not unreasonable to push around power switching transistors (would have to check the datasheet to see what the indicated devices would require), and with the generally lower efficiency of RF amps (compared to low frequency switching) and the relatively low power dissipation of switching devices (compared to total rated switching area), the gain may not be all that amazing.
These are the advantages of RF transistors: while they are more expensive and have small switching area (making them perhaps less efficient or powerful for class D/E applications), the drive power, and AC considerations like reduced parasitics (wide low-Z terminals, low capacitances, and especially low feedback capacitance), are optimized for exactly this application, of course.
You might even end up saving money against super speed gate drivers, or coupling transformers!
But 7MHz is still low enough that a discrete solution will do. Hams have been using ancient types like IRF540 for decades, at least in linears. Basically, count on having multiple stages between signal source (which is what, a logic-level clock or something?) and final.
Note that your circuit is probably okay below resonance, where it will behave as a ZVS class E amplifier (but mind the body diode recovery). Above resonance, it will probably blow up, because the leading phase angle of the (capacitive) load will leave some voltage on the drain, by the time of the next gate rising edge. So turn-on sees a momentary short circuit, dumping current from one transistor, through the resonant capacitor, into the opposing body diode.
As far as "mind[ing] body diode recovery", you need t_rr << t_cycle. This should be easy enough in low voltage types, but won't pass for, say, >200V MOSFETs probably. (Body diode recovery performance tracks inversely with rated voltage.)
Tim