In my experience, the Class C boxes work only marginally well on AM. That depends on a couple of factors. For one, that the operator knows how much input to give the amp and not over-drive it. The other is that he is keeping his modulation just below 100%. Those two things make a big difference. Not that it would be truly clean; but at least somewhere clear and understandable.
Unfortunately, many AM operators don't know how to do that. They just plug whatever radio they happen to have into whatever amp they happen to have - and think that everything is just fine. Here is a news flash - it isn't OK. Sounds like trash. Don't kid yourself either - it really is trash. Not knocking it; just calling it as it really is. If you have ever turned up a radio or TV too far, what you get is audio distortion - and so will over-driven transistors distort an amp. More importantly, it can damage the amp. More amps get burned up by not running the right amount of input power from the radio to the amp - than any other reason. Just a fact.
However, the BEST operators use an AB class amp and know how to drive it. They read the amp's specs and follow it for best results. They are clear and easily understood and aren't trying to get every watt out that they can. It is the difference between doing it right, or just hooking things together and just hoping for the best. So what if the amp is a TX-400 and you get only 320 watts of clean power out of it? It will last longer, not overheat, not destroy the expensive transistors, and just sound and work better. Just another fact.
So - to answer the original post - I would say just run the AB class amp. Don't get all wrapped up and fall into the trap of obsessing with getting all of the power you can. Make sure you don't over-drive the amp - either. VERY important! So what if you don't run as many watts as another local does? Within a close distance/locally, the extra power adds/does nothing at all. The AB class will work outstanding on AM and SSB; but the class C amp will barely work OK on AM (if set up properly) and just work plain crappy on SSB.
When doing DX, then the same situation exists. If I had a choice to run a 150 watt AB class and a 300 watt C class, I would pick the AB class every time. 150 watts of AB power and making sure that the radio output is matched to the amp input requirements when DX conditions are in - is a winning combination every time. Even if your antenna isn't the best there is.
Base:
P/T COBRA 146GTL(Spare)
President Jackson
Turner +3 Hand Mic
Pyramid 25 Amp P.S.
Home Made Ground Plane Base ant.
If this is your base setup; then consider turning down the dead key watts of that 146GTL or Pres Jackson down to 1 watt swinging to 4 watts on AM. Then, turn down the ALC until you get 9-10 watts for SSB with 'ahhhh' modulating.
That 150 watt AB amp may have two MRF-455's or 2sd1446's transistors (they are basically both the same transistor under different mfrs/numbers). Those kind of transistors are very commonly found in many AB class amps. They are a very low drive transistor that are EASY blown if too much power is applied to them. On the other hand, they are excellent transistors for both AM and SSB so long as you input watt them correctly. In truth, one of these 150 watt/1446 2 pill amps will put out only 130 watts clean at ~14 volts.
Now here's a thought. You might consider selling the C class amp and getting an antenna with better gain. An antenna with real gain is like running an amp. If another antenna has more gain than the antenna you use now - this will make a HUGE difference when transmitting. A 1/4 wave antenna has 'unity gain' (no gain; no loss). But a 5/8 wave antenna will have as much as 5db gain over the 1/4 wave antenna - which is the equivalent of running a radio that has 4 times the power output of the radio you now use. That change ALONE makes a BIG difference. An amp can give you gain; but so can a better antenna.
It is easier to understand someone who is running clean rather than someone just stuffing an inefficient antenna full of garbled watts. Hooking up two amps together - just to attain more watts - shouldn't be the goal - IMO. The kind of plan you are proposing usually leads to the destruction of both amps - eventually. Not saying it cannot be done; but very difficult for a beginner to get the details right.
That decision is up to you.
Hope this helped you . . .