When you speak of magenta in the shadows I have to ask if you are using Epson ink or getting refills at the local refill joint like Walgreens or Cartridge World. More so when you say a friend has profiled your printer & paper. It reminds me of a very painful experience where I completely embarrassed myself only to learn better than using a 3rd party color ink refiller.). They can save you a lot of money when color management isn't critical. In photography, especially in portraiture, proper skin tone is critical.
A RIP (Raster Image Processor) is a program that is very much like Epson print driver on steroids in that it allows you to profile each ink channel individually- think separation & application. With Epson Print driver you have some control but with limitations but unable to chose where & when ink colors are applied. With a RIP like QImage or others, you have total control over each individual color.
My R3000 is a dedicated B&W printer based on Paul Roark's efforts & MIS Eboni inksets. Each channel is a black carbon ink or a dilution of (think M & LM or C & LC inks). We start with Black and dilute it to get different shades of black. But there is no color ink; no magenta, no cyan, no yellow, just black. A lot of us use a RIP named QuadTone RIP or QTR. This wonderful jewel allows us to create a profile that controls each ink channel exactly how we want it.
The problem you are experiencing is that you are getting green tints in B&W & magenta in the shadows. All very common problems that are caused by the Epson Print driver, not the printer. There is a slight chance the printer is at fault but doubtful. In most cases, properly created ICC profiles should resolve the problem unless your monitor is out of calibration & you are inadvertently adding those colors back in during editing. Also, perform a head cleaning & alignment followed by a print check. I don't expect it will change anything but these are prevent maintenance task that should be performed regularly that do affect print quality. Inspect each one for abnormalities & let us know if anything else is wrong. If you are using true Epson ink & not refilling at the local stores, my bet is the Epson print driver is at fault or your monitor is out of calibration.