If you have the knowledge to do this, then go ahead. Most of these features seem like they can mostly be done externally, save for a few things- such as the chat information.
In order to do something like that you'd need to be able to include information pulling within the Wii U side of it, and pass each client's NNID to the server in order to display the name with each message. Not even counting the fact that you need to be able to prompt input from the console, then accept, pass, and display it.
Then it boils down to the frontend for the Wii U side itself. This is the part that gets a bit tricky, which is why I asked you this initial question.
First of all, do you aim to restore the service? ... Or do you aim to create your own separate service?
The reason I ask this is because if you aim to restore the service exactly as it was, then the frontend is basically already all there for you. You'd just need to undertake the endeavor of restoring the app's features (which is easier said than done, but it could mostly be accomplished by patching the original external content with your own). The problem with this approach, is that you can't really add new features as there's no source to work with. Unless you want to try a decompilation of the app itself of course- but that'd take a good amount of time as well.
If you were to create your own service, while you'd have to create the frontend and all other Wii U side features yourself, there's room for adding and updating features at will. It's more work, but it also results in a product that you're able to modify with less restrictiveness (this is of course assuming that the TVii service did most of the client side stuff on the console itself, I've not taken a look at it so I could be wrong in this assumption).
Both of these approaches have their problems. The biggest ones they both share are the amount of time, and effort needed in order to gain progress. Like I said, doing this on your own would take vast amounts of time that you may not be willing to put put forth. Putting together a competent team is almost out of the question as well as most of the devs in the Wii U scene simply work in their freetime, so you wouldn't be able to easily find devs willing to shell out that amount of time and effort either.
None if this is meant to discourage you, I just want to properly inform people who wish to undertake tasks such as this the issues that they'll be dealing with
before they encounter them.