There is a filter in ACF that you can use to modify the capability required.
you can create a function for this filter, get the current screen and see if it’s for your post type and if it is change the capability to match a capability for your custom user role and post type
add_filter('acf/settings/capability', 'my_change_capability');
function my_change_capability($value) {
// get the current screen
// if your CPT change value to your capability
return $value;
}