Have had a quick look, yeh the Rio 240 is just under £300, but you're not allowed to get that one its MY dream tank, so no going stealing it!
only kidding, yeh bigger tanks are always better, just remember that if you're going to do EI then that means replacing 120lt of water each and every week! Thats a lot of water, the Rio180 would obviously only need 90lt changes far more manageable, just a thought.
As you say you have budgeted more for the tank so if you have it to spend then yeh get the Rio240, will make an excellent centre piece for a living room.
As you say it will cost more, re substrate, lighting, etc, but sounds like you're wanting to put in the effort so go for it. The Eheim 2224 should still do fine, EI tanks should be under stocked anyway. Just check where the heater on the tank is, think it might be inside the black box thing with the filter, need to make sure you can take it out and have it on the tank just on its own, I would have thought this would be possible, but worth checking all the same.
Hope this helps.
Sam