Also i'm not entirely sure the stabiliser/TPI settings will have a huge affect on V1 or the point from which you can abort a take off....
It does. A more rearward CogG reduces the amount of rear stabiliser trim required. This reduces drag. The benefit of this is two fold. Firstly aircraft will burn less fuel over the course of the flight (assuming pax don't all move to the opposite end). Secondly it affects V1 because it means more derate or flex is available (up to the regulatory max of 25% rated thrust). Less thrust equals a lower VMCG (minimum control speed on the ground with aerodynamic controls used only), and thus a lower V1.
Each takeoff is planed to have the most critical engine fail at the most critical point (V1), and the aircraft performance/ loading/C.G planned to give the best feasible handling/performance characteristics should it actually happen.
With regards to landing, the allowable trim range is actually larger forvsome aircraft. A larger wing area (flaps) and more energy into the G/A (at Vapp or Vref which are higher than V1/VR). My beast has the same limits, but as weight increases the allowable range increases.
As for each pax seat making a difference, it does. Every item has a balance arm and a weight associated. The balance arms are all known, but the weights are either known of assumed(pax/bag weight). Should the catering configuration change, or another crew member joins us, the load sheet start point of Dry Operating Weight and Dry Operating Index( the trim figure) need adjusting. As the plane is loaded up with pax and bags and fuel in differing locations, the load needs tracking to make sure it doesn't exeed any limitsin weight, or balance. For the loading of pax, the night before a department called load control will look at the booked load, and typical number of bags that get checked in. If its a light load, seat rows are blocked off to prevent a to far forward trim occurring as pax request seats "as far forward as possible". To make this task simple, seat rows are divided into bays. So when you next ask a cabin crew member to move, she may well have to check with the flight deck first. If its ok, they may well specifiy the seat rows I which you can move to. These seat rows form on of the bays.
Hope that helps.
P.s. I forgot to Mention that airlines can take a performance credit by using a more aft forward CG limit. This enables an 'improved climb' performance to be gained by using some of the runway length acquired as a result of less drag. This enables more energy to be taken into the second segment of the 'Net Take-off Flight Path' used for performance regulations/calculations. This can result in less obstacle limits or a greater climb limited weight(WAT limit). We always look to use improved climb, using excess runway for greater energy. To do this we try where not a full load, to seat pax towards the rear. The excess runway and less stab trim drag means less flap (drag) and more speed on the excess Tarmac. Thus more energy. Where runway excess length won't permit a full flex or derate, we actually use more thrust to enable less flap use and higher speeds. Obviously this can only be done to a certain limit, depending on runway length, wind, temp, QHN and dry/wet. Using full flex or derate actually burns more fuel in the long run, but lower EGTs prolong shelf life of engines and maintenance costs. It's a balancing act between the two. airlines don't just blindly seat pax at the rear to pee them off.
I did try to upload some diagrams, but computer said no. Sorry.