Is a fast acting high efficiency neutrino detector possible? Todays detectors rely on rare interactions (with matter), which makes them large and slow. Is anything much better even possible?
 A: I think it's probably more theoretical physics on whether detection methods are possible, though clearly neutrinos are of interest to Astronomers too.
The short and simple answer to your question is generally no.  There's no realistic magic bullet to Neutrino detection with any kind of consensus behind it.  That's not to say there will never be one, but there's nothing underway and not even any good theoretical methods beyond technical improvements of ideas underway (to my knowledge).   You might find the occasional hand wavy article, but those will be more hypothetical than realistic.
That doesn't mean that progress on neutrino detection isn't being made.    Progress is being made, but using methods that are already understood, requiring, as you said, lots of matter and sensitive detectors.
There are many fascinating aspects on Neutrino detection (fun reading, I'm glad you posted the question).  Types of Neutrinos and their origin and direction and varying momentum and their ability to change from one type to another and their mass.  Lots of interesting stuff going on and detection of them will continue to get attention and research money and detectors will continue to be built.  
Nice short summary of detection methods here.  Different methods are needed to detect different types.   
Two articles on the Kamiokande detector  (little dated).  hyperphysics article here and Berkeley article.
Article on Big-Bang Neutrinos, which are very hard to detect.
and some more recently built large detectors.
Explaining why alternative methods won't work get a little tricky, and I have only a lose understanding, but the general theme of something being only very weakly interactive, is that, you need a very large catchers mitt to catch or detect a few of them and there's no easy way around that.  Whether some kind of detection field could be built that will improve detection, all I can say is that nothing I read on this subject suggests anything like that is close or even theoretically proposed with any kind of consensus.
