Is there a standard icon for how the message should display?
No. Icons, in general, don't have meaning and are only relevant based on a user's previous experience with them. You should never use only an icon to convey important information.
We want our users to know that progress is being made, and ideally we'd like to show a spinner icon (there is some concern from our engineers about being able to reflect the results with a progress bar).
If you want to show progress, show a progress bar. A spinner implies to the user that something is happening, but if nothing happens for a period of time they can easily reach the point where they believe nothing is really happening, and will abandon their action.
The progress bar should show true progress if possible, using a determinate state progress bar:
But if there is an uncertainty to the process, there are standards for indeterminate progress bars:
Indeterminate bars animate to represent progress being made, but that the application isn't totally sure how long. Spinners just spin.
You can give an indeterminate bar a value too. So if you can take a "best guess" at the progress so far you can represent that while still showing an indeterminate time.
(Source: OSX HIG)
If we use that, I haven't found any examples of a spinner with a text message. We'd like to let them know that it could potentially take a few minutes. Is there a way to convey a longer text message as well as a "waiting" icon without the screen looking too busy?
Assuming that you application must download this information before being useful, there is no reason why you can't present a full screen message telling them exactly what is happening. Tablet's aren't small - you have plenty of space for a very clear message.
You should include those messages show the user is clear as to what is happening.
download bmml source – Wireframes created with Balsamiq Mockups
However if your application can be used, but just in a limited capacity, then you should let the user in. Don't block them from doing things that they don't require the download to be complete.
In this case you could just disable the actions that require the download to be complete. If the user taps them, you can either ignore the action or show a message that you're waiting for the download to complete. Another option is to use a small portion of the screen while the download is happening.
download bmml source
If the user is able to play with some options, but not all make sure they understand why those they can't work with aren't available.