The reason why you cant find any sources on this is that you seem to be confused about what development economics and those different schools of economics are. I will first address the confusion and then give you references for some of the sources you requested.
Confusion about different terms:
First, development economics is a positive not normative field. Following the
Debraj Ray and Clive Bell Development Economics, the development economics is defined as follows:
a subject that studies growth, inequality, poverty and institutions in the developing world
An important takeaway is that this definition implies that development economics (as well as a wast majority of economic fields) is a positive field. It is concerned with what is not what ought to be.
On the other hand both Chicago School and Austrian Schools nowadays do not exist as a separate positive fields but they are almost purely normative schools that do interact with positive economics through study of political economy (i.e. the field of economics that, among other things, examines what are implications of different ideologies on economic policy. See the ‘Political Economy’ by Peter Groenewegen or this investopedia entry).
Historically in their respective time periods these schools were associated also with some positive economics. An example of this would be the problem of socialist calculation debate where members of Asutrian school such as Hayek were heavily involved.
However, in present day those positive propositions of Austrian or Chicago school that panned out were incorporated into mainstream neoclassical theory and the schools for most part do not pursue any positive research projects.
Next in you question you seem to equate Neoclassical economics with Chicago school which is simply not correct. You should not confuse Neoclassical economics with Chicago school as Neoclassical economics is a set of tools rather than doctrine.
For example, Sargent is considered to be a representative of 'Chicago school' because of his ideological beliefs but his whole work is Neoclassical. At the same time, Stiglitz who is ideologically as left leaning and anti-free market as reasonably possible within the mainstream of the profession (we are talking about a person who praised Hugo Chavez) is also purely Neoclasical economist and would probably get a stroke if you would try to associate him with Chicago school or Austrian school both of which he criticizes heavily. Next, a firmly New Keynesian economist such as Gregory Mankiw is ideologically pure libertarian/classical liberal clearly ideologically influenced by Milton Friedman and Hayek, yet his whole work could not be further from Neoclassical economics.
When it comes to 'Neo-liberal economics' there is not even such thing within economics. The New Palgrave Dictionary of Economics does not even has entry for 'Neo-liberal economics' only for Neo-liberalism as an ideology, and certainly in political economics you might study how Neo-liberal ideology can lead to different economic policies but there really is not a 'Neo-liberal economics' as a proper sub-field or even school of economic thought.
Hence a big problem with your question is that you keep mixing positive approaches and sets of tools in economics such as the Neoclassical economics with a normative largely ideological and political economic perspectives that Austrian or Chicago school in present day consist of.
Now finally after getting all the above out of a way, if you want to get some resources on Neoclassical perspectives on development economics then any textbook will do. A large part of development economics consist of purely neoclassical models. A good source is a Handbook of development economics by Rodrick & Rosenzweig (2009). A large number of models presented in the book can be safely classified as purely neoclassical models (albeit definitely not all). An excellent example would be chapters in the handbook that focus on economic growth that are for most part purely neoclassical.
Furthermore, you can have a look at sources cited in the handbook to get to see even more Neoclassical models and perspectives on development economics although the handbook is quite exhaustive when it comes to the current research and thinking on economic development.
If you want to get Austrian or Chicago perspective on economic development then you really have to study political economy and not positive fields such as development economics.
For example, you can get some idea about the perspectives of Chicago school on economic development by reading Milton Firedman's Capitalism and Freedom, where he shares among other things also opinions on why Hong Kong or Japan successfully developed.
For an Austrian perspective you can read some of the works of Benjamin Powell who identifies as Austrian economist (although his academic work seems to be more or less neoclassical) who shares his thinking on political economy and development in books such as Out of Poverty: Sweatshops in the Global Economy (Cambridge University Press, 2014) or Making Poor Nations Rich: Entrepreneurship and the Process of Development (Stanford University Press, 2008).