Another possibility is the 5DII. Just browsing around on the websites of the local electrical shops, the 5DII with the 24-105mm kit lens fits in with my budget (just), but doesn't leave any overhead for extra glass. Is this a good option to consider?
Yes. Yes. Yes. Although I would personally go with body only, and get a 50 1.8 or 1.4, and, if you can afford it, the 70-200 2.8 or if you can only afford the F4 get that. Then if you want a landscape lens, maybe look into the cheap manual rokinon lenses for a wide angle. MF is fine for landscape.
BUT remember: If you go from the crop-sensor (7D) to the full-frame (5DmkII) you instantly lose a LOT of length. That is fine if you have the long glass to compensate, but you would have to buy that also. If you intend to shoot persons or birds farther away than comfortable shouting distance, you should add into your budget the price of the long lens (300mm) you will need just to compensate for the loss of the 1.6x crop factor. The good Canon offerings at that length are not cheap, and neither are the good off-brand lenses, really. You can always crop your photos in post to get closer, but that is more damaging to IQ than getting there naturally with your camera and glass. Not to mention it seems a little unsatisfying to have nothing big and beautiful in the viewfinder when you shoot.
On the other hand if you shoot mostly close-range sports (basketball, checkers, tennis, but not so much baseball outfields) and your birds are on feeders, but you do shoot lots and lots of landscapes and portraits, then the FF body is great, and even an advantage on wide-angle shots.