Here is the picture of front elevation

Wouldn't your Architect have examples, or know of some, since he studied architecture? What does "American Architectural precedence" mean? that a house has to be a replica of an existing house? At the turn of the century there were alot of "Kit houses" produced, many of which had casement windows

There are " crank out" Windows that look like double hung Windows. They are often used in second story bedrooms as a means of egress. They can be opened very wide so that you can exit through them.

Really all these rules for your own home , I would buy a piece of property and build whatever I like away from all these controlled plots

Architect says that casements are not appropriate for this style, and the ARB would not approve. I agree with many of you that these design guidelines seem excessive. New Albany Ohio is adapting the NA Country Club architectural standards with some minor exceptions/provisions across the whole village. Most of the NACC homes are Georgian, Greek revival, or some form of colonial revival type. Rural vernacular or farmhouses are also appropriate for my area.

This is my second attempt get a house plan put together. Previously, I selected a French Country home style, and they denied it right away.

I have inward opening casements, with inoperable transom above. My house was built in 1930 and is a "farmhouse". I live in Canada though. Gee, I thought the "taste police" were bad where I live!

The double hung window is certainly most appropriate for what you are doing. However you may be able to achieve a similar look with casement windows that are divided into 4 glass pains with one vertical and one horizontal muntin. But you would need to ask the village board if those are acceptable.

Here's another example of casements that have a double hung look created by their "6 over 1" muntin arrangement: [https://www.houzz.com/photos/rustic-kitchen-rustic-kitchen-burlington-phvw-vp~2148645[(https://www.houzz.com/photos/rustic-kitchen-rustic-kitchen-burlington-phvw-vp~2148645)

Honestly it doesn't matter if we say casement windows are appropriate or not, it seems like they simply aren't allowed in you neighborhood. If its really important to you, buy a piece of property where you can do what you want. If this neighborhood is really important to you, which I think is completely understandable, you'll have to trade your casement windows for the neighborhood.