Manual reset is required on power on
It isn't clear from the description whether your setup has a hardware problem or a software problem.  For example, the rationale for “I had to snip the RST leg from the shield” is unclear.

The comment in ladyAda's example, “Can alternately just connect to Arduino's reset pin”, means that it's suitable to hardware-reset the LCD at the same time the Arduino does a hardware reset.  If the “RST leg from the shield” that you snipped is the LCD reset pin, as opposed to a pin driven by the small tactile reset switch on the 2.8" mcufriend shield, you probably should restore that pin.  In other words, unsolder and remove the stub of the pin you snipped off, insert a new pin, and solder it in place.

Note, just reinstalling the pin might make things work.  It's possible the LCD is sitting there in a permanently-reset  state, due to its RST input hanging open.  It's also possible the library is already driving RST properly but that drive isn't getting through, due to the missing pin.  Whatever the case may be, with the pin in place you should be able to software-reset the LCD by pulsing A4.  (Ie, with consecutive digitalWrite() commands, in setup() and before shield initialization, take A4 high and then low, or vice versa.)

Edit: If A4 isn't available for resetting the LCD (due to its use as the SDA signal for I2C, per comment) you might try adding a jumper wire from the shield's LCD_RS pin (above A4) to an available pin, and adjust the #define LCD_RESET statement accordingly.  

In general, to add a jumper wire, strip about 5 mm of each end of a short piece of #30 wire-wrap wire.  Form a small hook at each end.  Hold a hook onto the solder of the pin you wish to attach to and briefly heat the solder, letting the hook sink into the solder.  If you don't have wire-wrap wire, use a single strand from some old stranded cable (eg, mouse or keyboard).  Use thin heatshrink tubing or a bit of stripped-off cable insulation to insulate the jumper.  To keep pins in place while soldering, seat the pins being worked on into an old disk-drive connector, or another shield, or if you have nothing else, an Uno.

In your particular case, an mcufriend shield on an Uno, no pins are available unless you co-opt one of the SD-card-slot signals.  But before doing that, it's probably worthwhile to try your original idea of wiring to the Uno's RESET pin.  Your jumper would run from J3's second pin (A4) to J4's last pin (Reset), installed on the LCD side of the shield.  You should be able to see the trace between the Reset pin and the Reset switch, when identifying the Reset pin.