Hi Matt,
Been reading this with interest, that and doing 5 different installations is the way I've learnt. Each one throws up it's own curiosities.
On the battery, it does sound like yours is well on it's way out. If you put a new battery on the existing controller it will work but be under the stress of constant 700w demand. This is a nominal current draw of 20A, so a new battery would, ideally, be capable of delivering 1.5 times this as a maximum, in order to minimise stress on your new battery. Yosepower have been a good supplier for me - shipping from a German wharehouse there was no duty to pay.
Think I might do it the other way round, change controller/display set up, get it all running nicely, then source a new battery.
I have an Ezee hub and this is speed control, so I run two batteries in parrallel to feed it. It's not subtle but it does get me round the Welsh hills. Here's the odd thing (mathmatically at least). Pas 2 gives me around 11-12mph on the flat. Pas3 will give me 14-15mph on the flat. So on a given journey (let's say 10 miles), as the system always runs at max current, then I will use less battery in pas3 than I will in pas2 as the journey takes less time. I KNOW, bonkers right?
In practice (I've done the same journeys in different settings) the best that can be said is that it doesn't seem to use more capacity in the higher setting.