The NORX documentation does not specify how to use it for intermediate tags, but I agree with Richie Frame that it could easily support them. Using intermediate tags in sponge-based authenticated encryption was considered by Bertoni et al., SAC 2011, see Section 2.1. Since NORX's mode of operation is derived from the same construction, I see no obvious obstacle.
Note that, on the other hand, Keyak explicitly specifies the concept of a session with intermediate tags, its implementation readily supports them and its security analysis takes them into account.
About the second part of your question, i.e., that Keyak "seems to be slow in the absence of hardware acceleration", there is no objective reason to believe so, since Keyak with its 12 rounds and full-state absorbing should be at least twice faster than SHAKE128. For instance, our current benchmarks confirm the comment of Biv, as Ocean Keyak takes about 1.8 cycles/byte on Haswell on a single core.
Disclaimer: I am one of the co-designers of Keyak.
However the specification makes no effort to add or describe such a feature, but the mode over the permutation can do this easily with minor modification. New domain separation constants and a fixed method of generating the tags are generally all that is required on the encryption side, decryption is more complex and may require special output formatting during encryption for it to work in a seamless way.
This would however add more complexity to the description as well as to implementations. If the designers had considered intermediate tags, they probably rejected it for simplicity. It is certainly possible that intermediate tags were not considered in the design process, as many of the other candidates also do not have this feature.