How to display list items store in different Web Application without REST?

I have an one intranet site, and one public site. These have different web application. I want to display Tasks list and also insert items in intranet site into public site.

I try to add XsltListViewWebPart into page of public site, but this just worked for displaying list store the same Site Colletion. The best way I know is used REST service and get data from Tasks list and display it into public site. But the cons of this way is not having the button New Item of the task, and we need to fill Task Items into Grid view to display it.

I want this Tasks List can work good in XsltListViewWebPart but I can't. So, please help if you have any ideas or the best solution about this problem?