Yes, it's difficult to trap the ball in TS, very often it's not possible. You can try only when the ball is coming from certain directions at certain speed. Definitely not when the ball is rolling down the inlanes, even quite slowly.
I manage to have pretty long ball times, sometimes even MB last a while. You have to learn the shots to avoid. The biggest offender is the left ramp: never shoot at it! Unless ball saver is on (skill shot or upper target), or when the ball is trapped on the right flipper or is moving very slow. I can also shoot at it (backhand) when the ball is trapped on the left flipper (the ramp must be left diverted to make it). Of course it's fun to go for Vengeance/Super Vengeance and keep trying to go for ramps. Sometimes I play like that too, but again: shoot a fast coming ball to the left ramp and you get punished often.
Basically when the ball is on the right flipper the bread and butter shot is the left orbit: this is also not an easy shot (yes, TS is hard!), but I believe it is essential to master it to do well in this game. It works fine even if not perfectly done: the ball does not make the orbit and comes back down, but it stays safe.
In TS it's also imperative to be good at dead catches: this is a way to reduce the risk when the ball is coming fast. Maybe you cannot catch it completely, but you can manage at least to reduce the speed and then shoot it back immediately in a safer way.
So, forget the left ramp for a while and see if there is some improvement.
About the Battlefield: I can say I mastered it. I repeatedly managed to complete it in one go (even from 70). In the beginning I position the kicker "half ball" away from the right end before the VUK throw the ball in the battlefield. In this way more than half of the space is covered. I almost do not move the kicker, the balls most of the time goes towards the right or the center area, so I do not even have to do nothing. When the ball goes to the extreme right is the best: the kicker (positioned as explained) barely manage to push the ball, so that the ball slows down a lot and then it's much easier to follow it. Yes, not so fun, but effective. Anyway it's impossible to keep hitting the ball with the edges of the kicker, so it will soon start to move fast again. But if you manage to do it sometimes, it slows things down and it helps recovering the control. Obviously the ball goes also to the left side sometimes, so you have to be alert to move there. But after hitting, go back to the explained starting position (unless the ball is hit straight up the battlefield, then of course its obvious it will be back on the left). It takes lots of practice, but I do not think the battlefield is super hard.