You can go down two routes:
A. You can use the new arms and buy the 1.5mm shorter shock body and 1.5mm shorter shock shafts.
B. You can use the new arms and use 3mm limiters inside the old type shocks. Do check if your car can still bottom out properly, but it saves a lot of money - in the end you can always decide to purchase the shorter shock parts later on.
Afaik the new shock tower is indeed not necessary, however I find the new rear tower nicer than the old one: The shocks are less exposed as it's lower, it's beefier so shouldn't hit your motor plate anymore and it feels as if the rear end keeps it's composure better through corners (no deep rolling, less weird snappiness). So I'd try the rear one (do run 3-4mm limiters in the rear end if the chassis doesn't limit the car's droop), and it'll give you the chance to put the new one on the front as well
