Yes, this is the solution and also proofs the system is wonky at best. I just fired everybody, literally all eight commanders and 4 council members, I only kept the spymaster and the marshal, at this point you dont need the other guys really, but I get back to that. The crucial part is these fellows are NOT nobles, just peasants I slapped some bagdes on, while commanders need to be landed, council members are still free. Thus they can be bribed with 80 gold which is nothing and you can put glitterhoof on the imperial throne. Works for me

Now the idea is you keep a peasant only council, hence everyone only needs the occasional 80 gold to vote for your chosen one and all is good. You dont need to buy all the votes, just enough.
Well, yes, you can do that. It will piss off your powerful vassals and prevent you from using any vassals that happen to have great stats as advisors, but if your only priority is to game the council and inheritance system, it is possible. It is not a universal solution, though, because it has very notable disadvantages.
Now you dont have any commanders exept your marshal and yourself, you may want to have at least 1 siege general, the others cann be supplied either through the holy order of the myrmidons which I have as a vassal and the papal guard which is also a vassal. If need be like you just stated, we can put in additional commanders if the things look bad, but thats hardly ever the case and you can teleport commanders across the map which i always do, the ai as well. Keep in mind the AI is also incredibly bad with education, the best real noble I have right now is 18 martial, and that guy is going to kick the bucket soon. In 3.0 I read martial 40 characters are not rare for players, take that as a comparison.
Maybe I am a bad player, but Martial 40 is incredibly rare in 3.0, even as a Germanic Norse Viking. Perhaps you are confusing Martial with personal combat ability?
Martial 18 is a very good martial stat for a commander, at least in my experience. In my Vikings-turned-Normans-turned England game where I use both Norse and Norman commanders from my realm (i.e. one of the better pools you can have) and the best invitable christian characters, the commanders range perhaps between 15 and 20. Anything above 20 is a snowflake in AI-educated guys and something you have to work quite hard to keep up as a standard in your own characters (and at the expense of the other stats, which isn't always ideal if those guys could be a ruler).
All that aside, I don't entirely buy your "solution": making your marshal a commander will usually prevent him from performing any marshal tasks - which can be a decent tradeoff, but not one without disadvantages. Having a competent marshal train troops in Constantinople will give you quite a few more levies.
As Byzantium you will quite often be required to and able to field two, three or even more armies at the same time. Sure, you can run those armies without flank commanders, but that will lose you battles or at least more men than you need to lose in battles. You probably also could micromanage teleporting commanders from army to army. Which has - besides its gameyness - the disadvantage of being incredibly tedious and hardly fail-safe (both because you can make mistakes here and because sometimes you cannot avoid all of your armies getting involved in battles).
Again: yes, you can do all that, and it will make dealing with the inheritance law a little easier. It does come at a cost, though, and therefore it is quite far from a perfect strategy. Which doesn't mean that sometimes, when you desperately need the empire to pass to your underage genius son, it can be a situational solution.