Ah, I agree about that and it's why I hate being uncertain if my OTA blocking works because I'd hate to be stuck with an update that finally breaks the rooting exploit or something of that sort. That said, however, from what I've read the 8.9" Fire HD doesn't need a factory cable to enter fastboot. No confirmation on my end of that, as I've yet to need to use fastboot and thus haven't tried it.
I do know, however, that KFFirstAide's method of rooting with the latest version of the software (downloaded from here: http://xdaforums.com/showthread.php?t=2096888 ) worked flawlessly on 8.4.3 for me. And those who tried the older version on 8.4.3 didn't report any bricking or anything of that sort, simply that the process completed but did not successfully root. I would assume, but certainly not guarantee or suggest to know with any certainty, that it puts the risk of bricking in the event it can't root the firmware version down to a low percentage. It may be worth attempting. But I definitely see why you're worried about it; I'd be hesitant, as well.
Good luck, and I hope someone who's had experience with 8.4.6 can come along and offer you some solid answers. I'd definitely suggest blocking OTA updates when you regain root, though. With OTA blocked, you can still manually download any updates you want (preferably after seeing whether it's capable of being re-rooted) and install them via usb, whenever you wish.
Did renaming the otacerts file seem to work for you? Nothing pushed through recently?