I don't brew wheat beers, but I've put several batches through the conical fermenters now. My pale ales are super clear when they leave the fermenter now.
My process:
Ferment fully, and give it a bit more time. This has turned out to be about two weeks for beers under about 6% ABV. I have an old ale at about 7.5% that looks like it will be the same time frame for this stage.
Chill to about 45F for at one to three days to get as much yeast to flocculate as possible, then drop the yeast (save/harvesting for another batch).
Chill down to carbonate temperatures. I've done both 35F and 38F with equal results.
Once carbonated, give it a few more days with the CO2 feed disconnected (from the carbonating stone) so that it has plenty of time to settle down.
Transfer portion to serving keg via closed transfer and then can the balance.
Keg goes right into keezer and is put on tap if there's a spot for it. If I have a batch of the recipe still on tap, then it goes onto the gas feed that is for the style/type and waits for the previous keg to kick. I'm putting my stouts and porters on nitro/CO2 mix these days, where the rest are typically on just CO2. Not sure what I'll put the old ale on just yet.
I would also recommend doing a SMaSH, or simple pale ale recipe, to see if it's your hardware or something with your ingredients that's the source. Also are you using any finings in the boil, like Irish moss or whirlflock tablets? Are you dropping the yeast before carbonating and such?
For the record, I was getting very clear beers when using kegmenters either with, or without, a fermentation chamber. Before getting the conical fermenters (Spike CF10 model) I would carbonate in serving keg. Now I'm able to carbonate in fermenter and can't see ever NOT doing that. Being able to move fully carbonated (and chilled) beer from fermenter into serving keg, or fill cans (or bottles if I decide to on a batch/recipe) is so much easier on me. It also means that as soon as the keg goes into the keezer it can be put on tap and glasses poured.