Share your squidmates' ink at the start, rather than slosh yours indiscriminately. It can make a big difference. It gets me to the extra block nice and quickly, a bit quicker than an envious squidmate, and I get to go around the back.
Sure, the purple team grab the Tower, but this is a tactical choice. I splat them from behind, barely facing their ink to start with, and get my Bubbler charged. If I'm not mistaken, I even open the battle with a quad splat. Nice!
Now we can ride the Tower ourselves. Or we can both hop off at a tactical point, bringing the Tower to a halt. But clearing the path ahead of inklings, and laying down a path of ink, can be a good decision too.
The same hop-on, hop-off tactic gets me splatted a bit later, but taking your opponents' attention away from the Tower is generally good. Indeed, the Tower trundles on without me, as squidmates hop on. This is a good time for a super-jump.
No purple inklings to be seen, just my squidmates, keeping the Tower moving and safe, all the way to the goal. Woomy!