Try not to specify component values to 6 decimal places, it just clutters up the drawing. I think the 50 ohms (R2) is soaking up the drive power. I would work on .55V foward bias so R1/R2 = 27.5/.55 with R1 400 ohms. Now the input circuitry can be used to match 50 source Z to whatever you think the transistors input impedance is. I do not see the need for the inductor in series with R1, it would be better in series with R2. The output circuit, 600W @28 V, actually 56V p-p or 600W @20V rms = ~30 A, the collector impedance is about .7 ohms, so you are trying to match this to 50 ohms using two sections, so each section must be a 1:8 transformation. So design two PI networks Zin = .7, Zout 5.6 ohms and 5.6 in and 50 out. Obviously, the "centre" capacitors can then be combined.
Frank