Consider getting that 300/4 IS used. A lot of people buy these longer lenses but rarely use them. That's how I got mine... Off Craigslist, the seller claimed he'd bought two or three years earlier for an Alaskan trip and only used it a few times afterward.
If memory serves, I paid $900 US and it looked like new (doesn't anymore!), was complete with case, caps and everything... even had a high quality 72mm B+W filter on it (which I promptly removed, but keep for occasional use when needed). I use it a lot with Canon 1.4X Mark II teleconverter, which can be found used for around $250 US. That TC has minimal effect on focus speed and image quality. And the combined cost if you can find them used might be less than the lens alone, bought new.
I use it extensively with and without the teleconverter... for wildlife:
300/4 IS + 1.4X II on 7D. f5.6 (wide open), ISO 400, 1/400, handheld.
And various sports...
300/4 IS on 7D at f5.6, ISO 800, 1/800, handheld.
The 300/4 with it's IS is definitely a good choice for hiking, handheld shooting. I got it as a backup to my 300/2.8 IS, but ended up using the f4 lens a lot more often thanks to it's portability, especially on longer walks!
300/4 IS + 1.4X II on 5D Mark II, f5.6 (wide open). ISO 1600, 1/400, on a monopod.
It can be a pretty nice portrait lens, too, when you have enough room...
300/4 IS on 7D at f4, ISO 800, 1/400, handheld.
300/4 IS on 7D at f4, ISO 1600, 1/6400, handheld.
Also works pretty well for BIF...
300/4 IS on 5D Mk II at f5.6, ISO 800, 1/8000, handheld.
300/4 IS on 7D at f5.6, ISO 3200, 1/640, handheld.
And you are right about it's close focusing ability.... closest of any of the Canon lenses over 200mm.
300/4 IS on 7D at f4, ISO 800, 1/1600, handheld.
When you get it, I hope you enjoy the 300/4 IS as much as I have! I definitely feel the versatility of the 300/4 IS is preferable to the 400/5.6.... With the 300mm plus a 1.4X, you've got both a 300/4 and an effective 420/5.6, both with helpful IS. No doubt the 400/5.6 alone enjoys a bit better image quality than the 300 + 1.4X. The longer prime probably will focus a little faster than the 300 + 1.4X, too. But IMO the shorter lens + TC is suprisingly good in both respects.