Alternatives to the neutrino in the beta spectrum? It is well known that the neutrino appeared to explain the power distribution in the beta decay spectrum. (see PSE)  


*

*What other explanations candidates were available?   

*It is stated that the recoil of the nucleus is negligible. However, do we
have measures?


NOTE : A vision from Allan Franklin's ideas would also be interesting.  
 A: To begin, let's go over the basics again.


*

*Any ensemble of two body decays in which the parents and children have the same masses in each event has a delta-function energy spectrum, or violates at least one of energy- or momentum-conservation. The fact that the beta decay spectrum is broad and continuous implies that at least one of the pre-conditions is broken.

*Because the beta decay spectrum comes almost to the two-body prediction, any third particle must be very light.

*Our particle detectors are sensitive to moving charged particles, and all the charge is already accounted for so any third particle must be uncharged.
These are the consideration that led Pauli to postulate the particle that became known as the neutrino. Each of these considerations has a conservation law behind it, so there is very little wiggle room.
We started detecting them (well, anti-neutrinos) in the 1950s, using nuclear power plants as sources that could be turned on and off. Pay attention to that. When many beta decays are going on (plant running hard) the Cowan Reines instrument detected a lot of events. When little beta decay was going on (plant idling), they detected few neutrino events. And we duplicate that experiment these days (Double Chooz has days of "two reactor off" data and weeks of "one reactor off").
We also detect the expected flux from the sun (once we admit neutrino mixing), and from accelerator sources (which allow us to test the theory of mixing and to measuring the parameters of the theory).

Nuclear recoil is known to be small because a fast recoiling nucleus would generate a signal in our detectors and they don't. Until recently a precise measurement of the nuclear recoil velocity was not possible, which is too bad because that is one way to access the neutrino mass. However, an effort to do this is now underway (and I got to see a talk on it at APS in April) by the Project 8 collaboration who intend to measure the cyclotron radiation of the electron in a magnetic trap. They have demonstrated the necessary precision in a testbed device and are now attempting to scale up.
A: I've found an historical detailed description in this book:
Controversy and Consensus:
Nuclear Beta Decay 1911-1934
by Carsten Jensen ,  
From 1911 to 1934, 23 years, a lot of ping-pong with the experiments and theories went forth and back. I will not try to resume the history and the book deserves a reading.
My textbooks, aged, only mention the winning Fermi theory viewpoint and my question was about the 'others' perspectives, because I've a strong feeling that something went wrong in the past.
Bohr opinionated in favor of Beck-Sitte model:  

He expressed great sympathy for the Beck-Sitte theory of beta decay,
  in which energy was not conserved, and took a very reticent attitude
  towards Fermi's theory when it was announced. Fermi's theory was
  victorious and Bohr came to accept the neutrino, but only in 1936 did
  he publicly give his full support to energy conservation.

The break of the spatial symmetry was a price to pay that, 'in due time', will have to be rethinked too, imo:   

Thus, even though Bohr was shown to be wrong regarding energy
  conservation, his remark that "one should be prepared for further
  surprises with the beta decay" proved to be prophetic.

But Bohr viewpoint, and the Beck-Sitte model, were never proved to be wrong, only dismayed, and faded away .
Since yesterday that I'm aware of an alternative viewpoint and I've the need to have access to a lab, which I don't, and make an easy experiment that was never done before. Only after that I can write it on open.  
The needed lab is pretty standard like the one mentioned here and in the the video 
Drop a line if you know someone interested and able to help.  
edit add:
I found that the alternative viewpoint I was pursuing was already unproved in 1951 by Davies and Grace.   
