Starting in November I started getting Error Code 116-2898 when I tried to open up the Miiverse from Lego Dimensions. After it came up in the reddit and it showed up in the Miiverse I desided it was time to crack down on it and find a work around. After searching I had not found it in the forums so I desided to post it here as well for reference.
Tldr; I blocked ttg-analytics-svc.cloudapp.net in my router to get the miiverse working.
At first I assumed the Miiverse was down and tried again the next day. It didn't work so I tried in a different game and it worked. It was the same for both the lan adapter and the Wi-Fi connection. I then tried at various points in game and discovered it stop working part way through the opening cut scene. Since I had a Lan Adapter for my Wii U I did a test where I unplugged the network cable from the Wii U before I launced the game and plugged it back in once the game suspended in the home menu and was able to connect to the miiverse. If I didn't disconnect the cable before reentering the game the game would then connect to the servers and the miiverse would stop working again.
At this point it was fairly obvious that the Lego Dimensions connection was blocking the miiverse connection. However there were still new post on the miiverse which meant not everyone was experiencing the issue. At that point I decided not to contact either tech support at it is not Nintendo's fault here as it work for some people in Dimensions and it works everywhere else. I also wasn't about to contact TT Games and try to explain to them why the lack of Miiverse which is a Nintendo service is their fault.
This lead to the next step or a plan of attack as the plugging and unplugging a Ethernet cable is annoying. Twice as much if you are taking screen shots for a walk-through of the minikits. That involved looking at the log files in the router and cross referencing it with the client list. The actual log I used was way longer to make sure I captured everything. It was easier to parce then I had expected because out of the 10 unique destinations 1 was from Asia (The account server), services were associated with Amazon.com hosting including the miiverse and the remaining 3 which only occured in Lego Dimension were at Microsoft. At that point I found out my router's site blocking under parent controls require a URL and an IP address will not work.
I then put a computer between the router and the Wii U and looked at the DNS Requests and got ttg-analytics-svc.cloudapp.net and ttg-title-storage-svc.cloudapp.net. As soon as I blocked both Lego Dimensions got an error connecting but the miiverse worked. When I blocked ttg-analytics-svc.cloudapp.net under the parent controls Lego Dimensions had no errors and I could use the miiverse.
On a side note I got to use my Nintendo Wi-Fi USB Connector. That thing has been in my drawer a long time.