So you want to build a Teensy Beats Shield?  That's definitely possible but here's my disclaimer...  It's not a beginner's soldering project.  The three major ICs on the board do not have leads, and can not easily be soldered with a traditional soldering iron.  You'll want a solder paste stencil, and at least a hot air soldering station.  I use a stainless steel stencil, and a reflow oven at the local makerspace.

I've ordered all of my PCBs from JLCPCB.  The main board is just over their 100x100 limit for $2 boards, so it's a bit more expensive.  I believe mine have been running around $18 for 10, plus shipping.  When order, also check the box at the bottom of the form to also order a solder paste stencil.  At JLC this costs $7, and will increase your shipping costs a bit.  The gerbers in my git repository can be zipped and used as-is.

I ordered all of my components from Digikey and Mouser.  The Bourns encoders were not available at Digikey, so I ordered them from Mouser, along with the pushbuttons, the DAC, charger IC, and boost converter IC.  I've updated the BOM to include links to the exact products I've ordered. 

I recommend placing the parts on the board in the order specified in the interactive BOM.  This starts with capacitor, then resistors, diodes, ICs, etc...  I like to arrange all of my parts bags in BOM order, in a cardboard box.  As I assemble, I take each part from the front of the box.  I also place the solder pasted PCB on a piece of wood so that I can easily rotate the board without disturbing the paste.

Use SMD tweezers or a vacuum pickup tool to place the parts according to the interactive BOM.  As you cursor through the BOM items, the location will be highlighted on the board illustration.

When placing the RGB LEDs, note that their orientation flips 180 degrees in each row.  In the top row, the rectangular die visible inside the chip should be at the top.

When placing diodes D1-D5, note that the footprint may not be exactly right.  When I first tested my board, I had several that did not connect on both sides.  I fixed this with a soldering iron and some additional solder.

The status and recording LEDs on my device are uneven in brightness.  So if you order your own LEDs, you may want to experiment with different current limiting resistor values for.  For example, my green LED is much brighter - possibly because it is new and the others are several years old.

When placing the Teensy 3.6, you'll need to either not solder, or snip off the 3.3v pin.  I've used this space to route the large 5V VIN trace from the power supply.  If using header pins, it's easy to pull out a single pin with pliers.

Do not place the Teensy, volume pot, headphone jack, microphone, power button or display connector before reflow soldering.

I recommend using a reflow oven, but in theory, you should be able to solder the board using a hand-held hot air station.  I used chipquik, leaded, no-clean solder paste, and the default leaded profile on our reflow oven.

It's a great idea to do some testing at this point, before installing the $30+ Teensy device.  At minimum, inspect the ICs for bridges, and check for continuity between the VIN pin on the Teensy and GND.  Also check the 3.3V pin to ground.  If you have access to a current limiting power supply, it's a good idea to test the power circuitry.  Initially the power will be off.  Install the power button, and when pressed and held, the boost converter should send 5V to the VIN pin.  There should also be voltage present at the PWR_BTN pin on the Teensy when the button is pressed.

Once reflow is complete, and some basic testing done, you may install the through hole parts.  These are straight forward if using the parts linked in the BOM.  To avoid having to cut off long header pins from the Teensy, I installed some additional pieces of the black header plastic on the corner pins.  This raised up the Teensy so the pins only protrude a small amount on the bottom.  Don't go too high, however or you'll short out on the back of the display.

My display came with header pins installed, so I used a female header to attach it.  This brings it to about the correct height to clear the Teensy.  This may not be necessary, but I removed the SD card slot on the back of the display.  It is not used, and is dangerously close to the Teensy pins.  If you are not able, or do not want to remove the SD socket, you could put a piece of insulating tape over it.

The display can be permanently mounted on 10-12mm brass or plastic standoffs.  10mm looks about 0.5mm too short on my board, but it works.