Sorry, I missed the part where you previously made white pinot from a kit so you obviously didn't press whole clusters in that case!
Pressing whole clusters with a bladder press should give better juice, but I have no idea if home scale bladder presses are up to the job. (I help to make white pinot noir and blanc de noir at a winery and we use a bladder press, but obviously on a larger scale). I seem to recall someone posting here a while back that they pressed whole clusters in their small bladder press, but I don't know if they commented on yield and quality. I don't think a home scale basket press would be successful for whole cluster.
For my
white pinot, I crushed (using my hand crank crusher-destemmer) and loaded immediately into my #30 (~7.9 gal) basket press. You can stop pressing when the juice gets too dark and/or a bit bitter tasting. I seem to recall from your pictures that you have a nice crusher-destemmer (with rubber rollers?) which should result in less tearing of the fruit and so cleaner juice that is less impacted by the skins. But even if your initial juice is pink, a lot of that color will drop out during fermentation and aging.
There is also the issue of scale - even if you can use your bladder press for whole cluster I'm guessing you'll need multiple cycles (depending on how much you want to make of course). My rule of thumb is that a 5-gal bucket holds about 20lb grapes, so by that reckoning your 80L/21gal bladder press will hold about 80-85lb grapes. For a juice yield of 150gal/ton, that's only about 6-6.5 gal juice per press load (and that 150gal/T may be optimistic...)
So to answer your question, I guess I'd be inclined to crush/destem and load into the bladder press in cycles - ie just crush enough for one press load, press out the juice and then repeat as needed.
