Are "a long way in the future" and "long ago" the best phrases or are there single words to describe these very common concepts? I am probably missing something obvious.
The best I can come up with for "soon" is "eventually", although that refers to an indeterminate amount of time rather than specifically a long period of time.
"long ago" is already pretty short though - counting the space, it has the same number of characters as "recently".
Similar to the "soon" case, you also have "historically" available in order to refer to an indeterminate amount of time in the past, rather than a specifically short or long time.
For soon, the antonym that comes to mind is later (as in the phrase "sooner rather than later").
I can't think of an antonym that does a clearly better job than what you and ncoghlan already came up with for recently. Earlier, before or in the past could work, but that depends on the exact time frame and meaning you're trying to convey.