Since you are going to have a container per user (for now I'll equate a user with what you called a user application ID), that means you'll have a storage account that can contain many different containers for many users. If you want to have the application have the ability to upload to only one specific container while reading from many two options come to mind.
First: Create a API that lives somewhere that handles all the requests. Behind the API your code will have full access to entire storage account so your business logic will determine what they do and do not have access to. The upside of this is that you don't have to create Shared Access Signatures (SAS) at all. Your app only knows how to talk to the API. You can even combine the data that they can see in that summary of content by doing parallel calls to get contents from the various containers from a single call from the application. The downside is that you are now hosting this API service which has to broker ALL of these calls. You'd still need the API service to generate SAS if you go that route, but it would only be needed to generate the SAS and the client applications would make the calls directly with the Windows Azure storage service bearing the load which will reduce the resources you actually need.
Second: Go the SAS route and generate SAS as needed, but this will get a bit tricky.
You can only create up to five Stored Access Policies on each container. For one of these five you create one policy for the "owner" of the container which gives them Read and write permissions. Now, since you are allowing folks to give read permissions to other folks you'll run into the policy count limit unless you reuse the same policy for Read, but then you won't be able to revoke it if the user removes someone from their "trusted" list of readers. For example, if I gave permissions to both Bob and James to my container and they are both handed a copy of the Read SAS, if I needed to remove Bob I'd have to cancel the Read Policy they shared and reissue a new Read SAS to James. That's not really that bad of an issue though as the app can detect when it no longer has permissions and ask for the renewed SAS.
In any case you still kind of want the policies to be short lived. If I removed Bob from my trusted readers I'd pretty much want him cut off immediately. This means you'll be going back to get a renewed SAS quite a bit and recreating the signed access signature which reduces the usefulness of the signed access policies. This really depends on your stomach of how long you were planning on allowing the policy to live and how quickly you'd want someone cut off if they were "untrusted".
Now, a better option could be that you create Ad-hoc signatures. You can have as many Ad-hoc signatures as you want actually, but they can't be revoked and can at most last one hour. Since you'd make them short lived the length or lack of revocation shouldn't be an issue. Going that route will mean that you'd be having the application come back to get them as needed, but given what I mentioned above about when someone is removed and you want the SAS to run out this may not be a big deal. As you pointed out though, this does increase the complexity of things because you're generating a lot of SASs; however, with these being ad-hoc you don't really need to track them.
If you were going to go the SAS route I'd suggest that your API be generating the ad-hoc ones as needed. They shouldn't last more than a few minutes as people can have their permissions to a container removed and all you are trying to do is reduce the load on hosted service for actually doing the upload and download. Again, all the logic for handling what containers someone can see is still in your API service and the applications just get signatures they can use for small periods of time.
