saguaros JoomSEF works out of the box. With or without cache and without any configuration.
I found that if SH404SEF is off, there was still the issue (image not shown)with articles on the frontpage (module showing items from category). This was fixed if I created menu items (menu single article) but this was of course not the way to go. Then I started playing with SH404SEF again and turned SEF off per component. In combination with the menu-items that worked and then I decided to uninstall SH404SEF and install JoomSEF.
My conclusion is that there is still an issue with masthead in combination with the module showing articles on the frontpage. Like the custom.css (.layout-blog div.t3-masthead .ja-masthead-detail{background-image:none;}) to show articles in a blog via menu, something like this is probably also needed for the module showing articles.
JoomSEF fixed this as well because it renames the URL to the category and that picks up the custom.css same as listing the articles / blog via menu item.
I think you need to contact SH404SEF to discuss a solution because they are one of the biggest out there for SEF and you need to have a look at css to fix the issue showing articles per category via a module.