Palawan is easy to visit for birding, and it should be possible to go for much cheaper than the quoted price. As Captain mentions, the easiest option is to stay at Sabang and bird in the Subterranean National Park. I think the tame Peacock Pheasant is still around (it was when I was there in 2009), and is easily seen around the Ranger's office next to the cave. Permits for the park can be bought from the National Park visitor office close to the pier in Sabang. Most people take a boat from Sabang to the Ranger's office but these do not leave very early in the morning (unless specially arranged). It is also possible to walk through the park to reach the Ranger Station - this takes a couple of hours and involves a few climbs/descents, but can be very good for birds (I saw the Peacock Pheasant along the trail, as well as several other Palawan endemics). A guide is not really necessary, but could be useful if you want to find some of the trickier endemics (Falcated Ground-babbler, Palawan Scops Owl, Palawan Frogmouth - but these are all possible independently if you have the right recordings!)
Costs of birding at Sabang is largely dependent upon where you stay - and this of course depends on the amount of luxury you prefer! There is accomodation along the beach which is fairly cheap. There is also accomodation a short distance inland from the town, which is slightly more expensive but is close to forest which can be good for birds. To get to Sabang, it is possible to hire a car from Puerto Princesa or to travel by jeepney. I think some of the hotels probably also offer transport from the airport. Apart from accommodation and transport, birding here should be really cheap (I think a few US$ a day for park entry and boats - it should be possible to check online)
Birding at Mt. Kitanglad is more difficult (and probably more expensive, although the price you have quoted still seems a bit steep). You will definitely need to hire a guide. There is accommodation part of the way up the hill, and you would definitely need to stay here for birding. The eagle viewpoint is an hour or more further up the hill from the accommodation. I have been twice - the eagles were not nesting either time, but I still managed good views of eagles on both occasions, but the views can be a bit distant and depend on a combination of luck and hard work searching treetops. Birding in the surrounding forest can also be very good.
Overall, for a short trip as you suggest I would recommend going to Palawan, which really is easy and can be done fairly cheaply. Kitanglad is certainly worth visiting, but probably better as part of a longer trip, and probably better if you have a larger group to share costs for accommodation and guides.
