First, the progress update video:

Here's where I'm at in tuning. I do have it flying much better than it does stock, but it still needs more work. ~Back up you current parameters before trying these.~ First, altitude hold is funky, and I'm yet to figure out how to dial it down, so I recommend flying in stabilize mode (manual throttle) indoors. Note that I am configuring using Mission Planner and using APM firmware v3.4.3.

Update the following parameters (full parameter list page):

ACRO_RP_EXPO and ACRO_Y_EXPO = 0
ATC_ACCEL_P_MAX and ATC_ACCEL_R_MAX = 59065.5
ATC_ACCEL_Y_MAX = 36000
If you want the motors to stop at zero throttle, MOT_SPIN_ARM = 0

PIDS (extended tuning page):

Stabilize roll and stabilize pitch: 5.983694
Stabilize yaw: 4.5 (default)
Rate roll and rate pitch:
P: 0.080
I: 0.080
D: 0.007
IMAX: 0.15
Rate Yaw: defaults

So try that and let me know how it goes. Again, these are not the most optimal PIDs, but better than stock.

If you can't get the motors to arm, check these:

ARMING_CHECK = 0
BRD_SAFETYENABLE = 0

Additionally, I have uploaded my parameters file for if you update the firmware and it won't do anything. I recommend manually editing your parameters using the info above, but if all else fails, here's what to do:

1. Backup your current parameters.
2. Upload my parameters.
3. Calibrate the accelerometer.
4. Calibrate the compass.
5. Change your flight modes back to whatever you had them before.