You start with the input impedance measured or calculated at several points across the frequency range. The match will be exact at these points and not inbetween. Therefore the greater the points, the smaller the error between them.
Then you need an LC network with the number of elements equal to or greater than the number of frequency points.
Then you derive the input impedance (a polynomial in S) of the network as connected to the load. This will have coefficients related to the element values stated in algebraic form, such as L1, L2, C1, and C2.
This will give you a set of polynomials at each frequency where you substitute the load impedance value at the frequencies.
You then solve this set of N simultaneous equations for the numeric values of the LC values.
With your power level the components will be very large to handle the hundreds of Amperes of current and many kV. They may be so large that they have a total volume greater than a m^3 especially when you have to orient the inductors to not have any mutual inductance.
Nuhertz makes a Zmatch program that does the calculations. It has a 20 day free trial period. If you are on a commercial project you can buy the program.
Another alternative for your antenna would be a several turn loop that is 1 m in diameter. This form of antenna was commercially sold some years ago for the amateur service. It had a manually adjusted capacitor. It is no longer sold because it had such low efficiency and the amateurs stopped buying it.
One further item is that the antenna impedance will be a small resistance in series with a very large and variable capacitive reactance. If you can make the antenna have a large diameter the reactive part will be smaller and less variable.
Another item to check for is the stability of your power amplifier working into the load. Even though it may work at the design frequency, the out of band reactance of the load may cause oscillations.