I am looking to create a Gantt chart for our Production process. This is a risk reporting process for a financial institution and it is run monthly. One key feature of most tasks and milestones is that they are defined in terms of business days of the month (BD), e.g.: Accounting closes on 5th BD, market value runs need to be finished on 7th BD, etc. Each monthly instance of this process needs to be analyzed separately, because each calendar month comes with its own business day count (also some major milestones like committee dates are often just floating dates withing the month rather than a BD number). Could you please point me to Project Management software that could handle this flavor of Gantt chart well? I have tried Microsoft Project and while it can do what I need nominally, it is far too clunky to be usable.
Check Teamhood as it has your mentioned features and it is free - https://teamhood.com/use-cases/project-management/
As a software developer I would guess that you won't find a solution that does exactly what you need and isn't clunky or expensive due to license costs and/or the need to fit your process to the tool.
With proper specifications of input data format and expected output, this might be a suitable task for a junior to medium level developer with sufficient knowledge of (or time to learn) some graphics library that's up to the job.
Given how much business stuff is being done by non-developers using Excel, even that might be an option, although I slightly cringe at the thought of having written that.