Hey @Interester I’m glad you are giving Haxe a shot. Your question might be more appropriate for the OpenFL forum because that would be the best option for a Flash refugee. I also was a graphic designer well-versed in AS3 who migrated to Haxe/OpenFL when the writing was on the wall for Flash. While there are many options out there, as I’m sure you are aware, there are lots of success stories of developers converting from Flash. Poptropica and FlowPlay come to mind.
There is no single overall map because each project has unique features and needs. One big question I would ask is how did you build your animations? Tweens: try Actuate. Spritesheets: try OpenFL Tileset/Tilemap or other solutions. Timeline: OpenFL can load swf at runtime as an asset, or else convert it to Haxe classes. That could be a big time consideration so you might do well to figure out your solution to that, along with whether you need to rebuild graphics. By the way, OpenFL supports SVG if your art style supports it.
It sounds like you maybe built your own game engine. Again, depending on your needs you might consider Starling or HaxeFlixel which have heritage from AS3. The latter is quite popular nowadays.
As far as the language goes, here is a concise summary of the differences between AS3 and Haxe. There are a lot of AS3 conversion tools but I have found that the Haxe compiler gives a lot of good feedback and it will help you to learn as you fix this and that. You will find that the OpenFL Samples repository can be a good place to get familiar with OpenFL, especially for building things from scratch.
I hope that helps a bit, and I hope to see you on the OpenFL forum!