I will usually go to a weaker cover ball under the situation you described.
If it's a high friction house before it starts breaking down it's just a more natural option.  I usually do not need to move outside, just stay in the area with a ball that's less likely to slow down too early.  Perhaps a speed dominant guy can get the stronger ball to carry, but that's not me most days.

Bigger Ball, as much as it pains me now to do. Once you've chewed up the heads you can ball up with a weaker ball and stay in the friction, but the bigger ball gives me the opportunity to stay more relaxed and push the ball into the friction with a soft hand. That's just me tho.

Bowl in an extreme over/under house and balling up usually worked better this past season as balling down would still over react in dry and then skid too much in oil.

If I'm trapped between higher rev bowlers and the dumpers, and the middles are still viable, I'm going to move way left, and get away from the traffic with something that changes direction quickly, like a Boost Pearl or Dream On, depending on volume.  On if the volume inside is heavy, and the track area is beat up. Boost if I need more push.

On heavier house patterns, I will actually move right with the same ball and straighten out my angles to keep myself in the shim, then make a jump about 3rd game with something stronger.