I'm not an expert on performance boats and certainly won't claim to know half what the guys at BMC do but I'll air my thoughts anyway!
Steering: Assuming the helm pump is correctly matched to the cylinder, which at 2.1cu sounds like it is, then it's fairly safe to assume this is not where your problems lie re heavy steering. The Seastar pro system is suitable for your application and certainly up to the job.
As far as weight distribution is concerned, we don't know how much extra is in the reinforced transom but I doubt it's a significant amount, not enough to ruin the boat anyway.
So what's left to look at?
Engine height: I know performance boats run with motors set higher than the usual 2.5cm above keel but 8cm at the lowest? Assuming your CMC gives 5" (12.5cm) of travel that means your range is from 8cm right up to 20cm (8")
Sounds really high to me, has the jack been fitted to allow you to move the engine down on the jack, or lower the jack on the transom? Worth a try I think.
Engine offset: I can't be bothered to work out if BMC moved it off centre in the right direction, I'll assume they have. But 30mm doesn't sound much for a 300 hp motor. Saying that I don't think the effect of going another 10-20mm would make a "massive" difference.
Prop selection: If I had to put money on it, I would say this is where most of your problems lie. I've experienced how heavy steering can get with the wrong prop, you would be suprised. It can also effect how the boat steers, eg start a turn and the prop can try to tighten the corner forcing you to have to forcibly pull the wheel back to centre.
I'm not that familiar with all the props you mention, but some I think are stern lifting props designed for bigger, heavier boats. This could be causing the back of the boat to get skittish, something like a Laser II might be worth a try, it's a fairly predictable, standard issue powerboat prop designed more for giving bow lift. I don't know much about your hull design, if it is very performance oriented then you can expect it to get flighty under certain conditions, specially when you back off the throttle at high speed.
With a set up like yours you need to accept that there's a trade off for all that top end speed and it's going to demand more user input with the controls to get everything right and allow the boat to perform properly.
With the addition of variable engine height as well as trim in/out, it's going to take a long time to get to know the boat and learn to interprete what she's telling you.
Getting your hands on as many props as possible to try out could be one of the keys to success, unfortunately you've shot yourself in the foot buying a counter rotating leg, although if you can find the right ones second hand they tend to be much cheaper. Pairs of props often get split up to use the RH, leaving the LH sat on the shelf gathering dust. The other problem is CR legs tend to wear out much quicker than RH legs, something about direction of the thrust acting on bearings etc.
I'd also suggest getting on to the Scream & Fly forum
and repeating yourself there, there's a lot of guys there running the type of set up you have (just without the tubes) and might be able to offer advice.
Hopefully that gives you something to think about