Hi Don,
While I have always enjoyed Whitman's poem, the guy wasn't exactly a raptor biologist. In fact, there was no raptor biology back then except among the falconry community.
To my knowledge, and as romantic as the idea might be, eagles don't mate in the air. I've certainly never observed it. Some other species (e.g. swifts) are known to do so but not raptors. This might be a good thread for Tweeters....birds species that DO copulate in the air.
What you are seeing, in contrast, is literally a battle to the death. And alot of them do die as a result of this behavior. They often slam into the ground because neither one will let go on the way down. Perhaps one wants to but the other is either remaining in an aggressive mode or simply panicked by the rapid and often twirling descent.
There are many records of this phenomenon. One guy I knew had two locked up adults slam into his garden on Orcas Island and sit there claws entwined for over an hour near dusk. They literally had to separate them by hand (and flashlight) as you did. I think it clearly illustrates how tenacious Bald Eagles (maybe all the sea eagles) can be during an aggressive interaction.
To me, it is another example of some evolutionary fine tuning needed in the raptor world. It is right up there with peregrines repeatedly choosing a wet ledge every year and their eggs drowning in a puddle of rain. You'd think that behavior would have been selected out long ago but it hasn't.
Perhaps in another five thousand years Bald Eagles will have the equivalent of a ground proximity sensor hard wired into their nervous systems.
Oh well...

Bud Anderson
Falcon Research Group
Box 248
Bow, WA 98232
(360) 757-1911
bud at frg.org