I think there are two solutions in your list that fit your use case best; the read query before the update (solution 2) and sending an update token with the read request (solution 5).
If you're worried about performance, I'd decide on one or the other depending on how many reads vs updates to a resource you expect. If you expect way more updates than reads, then obviously solution 5 is better, because you don't need to do an additional database fetch to figure out the owner of the resource.
However, you shouldn't forget the security implications of giving out an update token. With solution 2, assuming authentication is secure, then updating a resource is probably also secure because you determine the owner of a resource on the server.
With solution 5, You don't double-check the claim the client makes, except that you check for a valid signature. If you're letting the update happen over a cleartext link (eg, no SSL), then only encoding the resource and user id in the token isn't secure. For one, you're opening yourself to replay attacks, so you should include a nonce that grows with each request. Also, if you don't encode a timestamp/expiration date in the update token, you basically give indefinite update access to anyone who has that token. Finally, if you don't want the nonce, then you should probably alsoat least include an hmac of the fetched resource, so that the update token is only valid for the state of the resource as it was fetched. This makes replay attacks more difficult and further limits the damage knowledge of the update token can do, since the update token is only valid when the resource is in the given state.
I think that even if you're communicating over a secure link, adding a nonce and maybe also(or at least an hmac of the state of the resource) and an expiration date for the update token would be a clever thing to do. I don't know the application domain, but you may deal with malicious users and they might wreck all kinds of havoc with the power of unlimited update access to their own resources.
Adding a nonce will mean an additional column per resource in your database where you store the value of the nonce you sent with the last fetch request. You can compute the hmac over the serialized json representation of your resource. You can then send your token not as part of the message body but as an additional HTTP header.
Oh, and I'd use a token, not a URL; in REST, the update URL for a given resource should be the same URL the resource was fetched from, right? I'd move all authentication & authorization-related stuff to the HTTP headers, e.g. you could provide the update token in the Authorization Header of the PUT request.
Note that adding a nonce will also require a database update (the new value for the nonce) for each resource fetch request, unless you want to keep that information in transient memory and simply have the clients retry when your server is restarted between a fetch and an update request.