I too have similar requirements. Actually my wishlist is bigger. Few things I could change/work-around… and I did that. You can have a look here I have written many Tampermonkey based browsers scripts in the past to work efficiently with Zerodha Kite. I am sharing some of them with the community today, hoping they help others too
The web is malleable. It is possible to create some fix for your mkt-depth req in kite. You can open a popup chart window but hide the chart and just show mkt-depth from a user script or a browser extention. But the best solution will be if Zerodha gives a good desktop app.
It is frustrating to see no broker is giving a good desktop app for “trading”. 