Filament Spill Number 354, please help. (Page 1 of 2)

So when this problem occurs does the filament still exit the extruder? Or does the filament stop exiting through the nozzle and the above happens?

Well I see the idler arm is cracked at the fulcrum point which means you have too much pressure being put on the filament. The next issue looks like your tube is not being installed correctly and internal pressure is pushing it up to the point where the hop gear grabs it bends it sideways which is when the filament also starts coming out.

The idler should be adjusted to where it puts just enough pressure. The Hob goblin should not need near the force applied by the idler that other gears need to bite the filament.

I would also like to see a picture of the space between the nozzle and heat block.  Also a picture of the space between the top of the heat block and the cooling fins.

Note: You mention that you ran the temp all the way up to 245.  That is not really that hot for and E3d or the filament that you are running.  Try running it up to 280 and let it sit for a minute.  Then try pushing filament through by hand to see if it will push through.  If it pushes easily then bring the temp down to normal (About 245 for ABS) and see if it will still push through.

Cleared the nozzle, put in new ptfe tubing, cut it to just barely clear the extruder drive gear and idler bearing... set extruder to 245, extruder speed to 100%, extruded 100mm okay.

Ran a a little print job, filament spilled again.

I'm seriously about ready to toss this thing in the holler. All I can think of now is to have a print hub make me a piece that completely encapsulates the gap between the drive gear and the top of the barrel.

+1 to wardjr Speed can definitely be an issue.
However, I would like to point to the tooth gouges in the filament. The Hobb Goblin obviously has very sharp teeth. It is designed this way to pull very rigid material, so ABS gets deeper indentations than say polycarbonate.

You need to loosen your tension arm a bit no matter what mount you are printing with. The gouges are catching on the PTFE (this will happen no matter the tube length) and snagging. The mdroman mount is not aligned properly for the Goblin, but even with the wardjr revision, the filament will snag on the liner pushed all the wall to the gear if the filament has significant ridges for it.

Edit: I can't read. That doesn't look like the right hotend mount to me though to be honest.

You can also heat it up to 280 (go slow so you don't overshoot) and let it sit for a couple of minutes. Then extrude while cooling down to 245.

Regardless of whether the nozzle is clear or welded shut, the filament shouldn't be able to squirt out (aside from maybe Ninjaflex). I would expect the filament path and drive gear (Hobb-goblin) to be able to hold all the way up to the stepper motor skipping steps.

I would focus my efforts on ensuring the filament path is straight and aligned, and that the idler bearing touches the filament at the 3 o'clock position of the hobbgoblin, not the 2 o'clock or 4 o'clock positions. If the bearing is not aligned properly, it will cause the filament to squirt out as the force vector is not vertical.

If memory serves, the Hobb-goblin needs a different idler bearing, idler arm, and mount as compared to the original SD drive gear.

You have all the experts (No kidding, these guys are the best and brightest) trying to help you. 
The helpful thing (to others reading this) would be to answer this question or ask if you don't know what I am asking for.

It would be the highlighted number in this screenshot.  You should know what it is as it would have been something you changed to upgrade to the Hobb Goblin.
Your number will be much lower than mine and it would be helpful (to those of us helping) if you try and provide direct answers to the questions being asked.
 

We are all here to help and understand how frustrating problems like these can be.
Perfect alignment of all the components is essential to ensure the filament isn't getting an opportunity to flex out of the way.

Just a random though:  Is it possible that what you think is ABS Filament could be PLA or something else?

That screenshot is of the jog speed, which is the speed that material is extruded when clicking the Extrude button on that screen. You need the steps/mm of the extruder axis, which is in the firmware settings. You can get those quickly by sending a M501 in the Communication tab.

151 steps/mm should be in the ballpark. Have you confirmed by measuring 100mm of filament above the stepper, extruding 100mm, and checking how much was pulled in?

Maybe I can remove the nozzle and measure the filament feed distance.