Time to try a full reboot and burning insense while turning around three times ...
All wireless is voodoo.. so I am glad to see you have thrown away your scientific manuals and howtos.. and reverted to black arts. Unfortunately printer wireless is like voodoo with gremlins on top.
I have never ever been successful with pins and WPS and whatnots.. I am old school.. I do it from first principles.. use the printer utility.. in the printer utility there is a method of setting wireless to Infrastructure mode.. this is vital.. it will not work in adhoc.. and you can set wireless name and security settings of the AP you use.. remembering of course that it is SMB compatible.. short, no spaces and pure alphanumeric.
After setting up a brother on a Mac.. and beating it with a large stick for a couple of hours.. (figuratively) I won.. in the process I deleted the printer settings in the Mac and started over from scratch half a dozen times.. (after offering of incense and chicken livers).
"This type do not come out without prayer and fasting".. you need to exorcise the demon.. (gremlin) to manage only the wireless voodoo.
BTW.. i use ethernet for all printers.. never again will I use wireless. I buy network printers with real printer network cards in them.
I recommend you get, borrow .. invite over friends with PC laptops who know something about networks.. and get them to setup the Brother from PC. Frankly these things are designed for the windows world.. it will usually work fine in the Mac.. but the setup has to be done in a PC.. and seen and known to work in the PC. Apple is still too small a market for printer manufacturers to worry if it works with all bells and whistles.. also Apple keep changing the OS and the old drivers stop working.. lots of printers that used to work up to Lion gave up the ghost on Mountain Lion.. for no good reason.