Try saving up enough of a load to fill the basket at least 3/4 full. And make sure you're keeping fabric weights sorted, such as normal t-shirts, socks and underwear, and light fabric pants, like track pants, all in one load. Keep anything heavier like hoodies and sweaters, jeans and pants, and the like all in their own load. As far as whites and towels, wash only towels, dish towels and wash cloths together, and keep the white shirts socks and underwear on their own. The Oasis machines are finicky if you have all different weighted fabrics together, and I'm sure the LG will be similar. The heavy items get stuck on top because the light weight items just drag back and forth underneath as they don't have the heft to cause much turbulence against the impeller.
Then, try using the Normal cycle with these full loads. Adjust your detergent to an estimation of the size of the load and how dirty you feel they are, not how much water you anticipate. Most HE top-loaders use a gradual procedure for filling because of the soaking they do at the beginnings of the cycle, so you won't have to worry whether the detergent is getting a good workout. I'd add whatever options you'd like as far as rinses, whether your machine has Fabric Softener options or just "deep rinse" buttons and what-not. And see if you have any improvement from there.
I found with the Bravos that the PowerWash and Heavy Duty, and especially the Bulky cycle, were indeed NOT the best selections for the majority of loads. For example, both the PowerWash and HD cycles use a tiny bit more water, and add alot of spray and soaks during the wash, but the agitation doesn't change, it's the same 360 degree oscillation through out. If the items in the load aren't uniform in weight and shape, such as towels, there just won't be good rollover. The Bulky cycle, while using a 3/4 tub fill, does nothing more than ball the load up into a tangled mass that thrashes about, and then causes terrible off balance spins that have to be redistributed. After a while I finally gave the Normal cycle a chance with everything but towels, and because it spends so much time presoaking and spraying at the beginning, and then washes with agitation that varies from aggressive nearly-540 degree rotations, stepping down to barely half-turns to even the load out, then steps back up to medium and aggressive again, the load moves around beautifully, and has yet to get tangled or cause imbalanced spins.
I hope I'm not coming across as a know-it-all, and I know we have different machines, but just figured I'd throw in my 2 cents from my experiences so far with mine. Hopefully it may help turn the experience you've had with your machine around as well.
