It is a good idea to have played chapter three through a few times so that you are familiar with the landscape, Taken attacks, and tricky sections. This way you will be aware of big ambush locations, bottlenecks, and how much you'll likely need to ration your ammo (as well as how much of the good stuff you'll end up with).
The key piece of advice is to handle this as you would the 'Gunless Wonder' achievement or a run through on Nightmare, i.e avoid every fight if at all possible, stay in the car as much as you can, and RUN. Large packs of Taken can be largely avoided through smart use of flares or by a well aimed/timed flare-gun/flash-bang shot, and poltergeist objects can be dodged and eventually outrun, so don't waste time and ammo on them unless you absolutely have to or have managed to get penned in.
Don't waste time on collectables or out of the way chests and only go for 'safe chests' - namely the ones which don't come with a nasty Taken ambush - if you feel you need to. When you reach the train yard, there is a car at the exact point where you drop down. Use it. It will shave a large amount of time off your run and save priceless ammo and risk of death. Hop in, drive to the end of the yard and park up. As soon as you hit the switch, jump back in, ignoring the poltergeist objects and Taken and drive for the end of the yard where the broken fence is, ignoring everything, but avoiding a head-on with poltergeist stuff if you can. Don't worry if your car gets bashed to hell before the end, just bail out and run... as soon as you jump over the broken section of fence, no Taken can reach you or will follow you, so don't bother fighting and just make this your goal. The dodge move will be your friend here!
The other big panic sections are the large Taken smashing down the door at the top of the mine (flashbang him for a swift exit, don't muck about) and Cynthia Weaver's old mansion. The mansion is the last big hurdle and is a royal pain if penned in. It will essentially be a bottleneck of Taken as you fall through the floor and have to get back up to the top again. Don't waste time fighting here... you won't need any gear from this point, so if you have flash bangs, then use them to clear your way to the stairs, or if you have flares, drop them. But don't fight, run. Head straight for the stairs (it can be easy to get disoriented in the confusion) and run up. Drop a flare behind you if you're panicky and keep going. Be careful how you jump the gap - you don't want to fall back down there - and drop down off the roof. Now breathe. And run.