Chad Orzel has highlighted a couple of papers (one still a preprint) on the issue of quantum tunneling time or speed. I missed these, just like him, but unlike him, I didn't have as glamorous of an excuse - I was busy finishing up teaching a summer physics class.
I'll let you read have the pleasure of reading his article, because he also gave a quick background on the quantum tunneling phenomenon, if you're not familiar with it. But as background information, I did quantum tunneling spectroscopy measurement for my PhD research and dissertation. So I'm familiar with this, but not in the sense of the detailed question on tunneling time. We simply used the phenomenon to measure the properties of the material of interest, even though in the end, I ended up looking into the detailed description of the tunneling matrix elements, which are often simplified or ignored.
Still, the issue of tunneling time has always been something in the back of my mind, and the question on whether this thing happens "very fast" or "instantaneously" (just like quantum entanglement) has always popped up now and then. It is good to see new studies on this, even though the combined conclusion out of these two results is still uncertain.
1. N. Camus et al., Phys. Rev. Lett. 119, 023201 (2017).