Soooo the problem seems to be that your Wordpress post has HTML classes, which are successfully being pasted to the Discourse post (as is shown in the raw HTML you posted from Discourse), however, when Discourse is displaying the post, it strips out the HTML classes:
And this is some more info on creating a plugin to make this happen:
I’m not sure what the easiest solution would be for you. I personally wish it were much easier to whitelist HTML classes so that we wouldn’t have to create custom plugins each time we want to whitelist an HTML class.
If you can figure out how to make the classes not get stripped when the post is displayed, then after that you’d have to make sure that Discourse has the proper CSS for the HTML elements you have on your Wordpress site.