Sorry to say, but it sounds like you’ve got a no-bueno situation. White grapes should always be pressed as soon as possible after picking in order to reduce juice (and subsequent wine) browning. By letting your white grapes sit overnight (and they’re juicy after being picked, especially at the lower levels of your buckets or bins) you started what effectively was a whole-cluster maceration and the juice began extracting compounds from the skins that can become brown. Grapes naturally contain an enzyme called polyphenol oxidase, which can start an oxidative chain reaction in grape juice that turns normally colorless compounds in the grapes into brown pigments.
By macerating your grapes overnight you increased the concentration of the available substrate so it isn’t surprising that when you did get around to pressing the juice, it was brown, and that the subsequent wine is brown as well.
It is completely normal to experience some browning when pressing white grapes, even those pressed immediately after being picked. At normal, low levels these brown pigments fall out of solution during primary fermentation and the resulting finished wine is normally of the pale yellow or green color you are thinking of, as long as the fruit was clean (no microbial infection), 30 ppm (or so) of SO2 was added to the juice and no excess oxygen was introduced during pressing, fermentation, racking or storage. My guess is because your juice was so oxidized from the start, it just couldn’t lose its pigment load.
So what can you do? Sterile filtration, or just passing it through a tight pore filter (like 0.45 nominal) will not remove brown color as most of the pigment compounds are so small and will pass right through. I suggest trying to fine your wine with PVPP (polyvinylpolypyrrolidone) or even activated carbon as a last resort (since carbon can really strip aroma and mouthfeel). During the tough 2011 vintage, when California experienced a lot of microbial pressure from rot and molds (which can exacerbate the polyphenol oxidase browning reaction), winemakers had success throwing a “kitchen sink” of fining agents at their white wines. An example of this kind of broad-spectrum fining agent is Phenol-Fine that is sold through American Tartaric Products, though many other winemaking supply stores and companies carry similar products.
As with any fining process, do bench trials on a small volume of your wine first, in order to get an idea of how much finings you need to add to achieve your goal (reduction of brown color) without completely stripping your wine’s aroma and mouthfeel. Good luck — next harvest I bet you’ll be willing to pull an all-nighter, or at least get started crushing earlier.