Linear Technology parts do tend to be a bit on the spendy side. If you ask them nicely though, they will usually send you a couple of samples free of charge. I've used the LM257x parts as well, originally National Semiconductor and now cheaper clones are made by TI. They work very similarly to the LT parts but do double check the pinout and current rating.
The inductor is really not all that critical. They only come in a handful of standard values and most of these integrated switching regulators will work fine over quite a wide range of inductances and in this case a similar application recommends 150uH so I would expect anything from 100uH to 200uH to work just fine and a much wider range is likely to work to some extent. If you are trying to optimize efficiency then you want to get the value a bit closer to ideal, but here you are just trying to diagnose and I am betting there is nothing wrong with the existing inductor.
Same with the diode, it's not critical. Any Schottky diode of equal or greater current and voltage ratings will work fine, although if the diode tests ok out of circuit then it's highly unlikely to be bad.
There is just not much to this circuit, and most of the parts are easily tested. There is no need to shotgun it and replace everything.