I’ve requested a support ticket on this topic but thought I ought to share it here too in case it is affecting others.
When selecting ‘Page Attributes’ under ‘Supports’ for a new custom post type, there is no option under the ‘Page Attributes’ section on the editing page to select a new custom page template (or switch between the theme templates). Only the page ‘Order’ is shown, with the option of changing that.
This isn’t fixed by making the custom post type hierarchical. I’ve tried this on a completely fresh WordPress install, with several default WordPress themes and can’t find a theme / plugin conflict going on.
It’s a shame, as it’s otherwise great to be able to work with custom post types and fields all from within the same plugin. Anybody having the same issue?