How to safely transport external hard drives during air travel?

Quoting this, this, and this:

External disks are no different that internal disks, in terms of media and components. Laptops have been going through X-Ray machines for decades without incident, so I see no issue with external drives doing the same safely.

It seems you have done your homework already. The most crucial part is to avoid shocks which is why it is better to handle it yourself.. Turbulence can occur regardless, so it is best to keep hard disk drives padding in bubble-wrap or foam. An anti-static bag would also help with an unexpected electric discharge, just to be safe.

The only additional caution I can suggest, is keeping them off. This parks the head and is safer. On most flights though, a hard-drive will generally operate safely as the cabin is pressurized quite well on modern aircraft except for very small ones. When the pressure goes below about 68kpa, small-platter (2.5" & 1.8") HDDs often fail. A 3.5" one usually work as low as 56kpa. This is why there is a maximum altitude rating of 10,000' for small drives and 15000' for standard ones.

You can also use storage case bags that are specifically designed to carry external hard drives such as this one:

Been travelling worldwide with my 3 Samsung 500 gig HDD's for over 5 yrs now and never experienced a problem. Airport scanners include LAX, JFK, HKIA, Ben Gurion, and the dreaded "heathrow" (don't go there!!).

Modern hard drives put their heads in a safe position when the device is powered off.

This reduces the chances that moderate shocks damage the platters, contrary to what happens when a spinning drive is shocked.

As pointed out, the shock required to damage a hard disk that is powered off is enough to show visible damage. The disk may have to call from the baggage store towards the floor. At that point, a lot of different hardware will be compromised as well.

I still recommend bubbles anyway.