I haven't see that you have added magnets, personally (it's just my opinion) I don't think is a good idea, because magnets saturate your core and the flow will vary very difficultly, magnet provide DC polarisation, DC polarisation saturate a core and draw a lot of current with in result a very low induction, but you can test it with also, why not !!!

Magnetic flux does not transfer energy the electric field transfers energy

I am thinking of making a higher powered BITT from off the shelf materials.
Is there any reason why this idea wont work.
I may change it to have one thin cut right through the middle leg to halp the BH curve be more linear.
But this is the basic idea.
C:\My files\FE\BITT\bitt draw1.jpg

http://www.themeasuringsystemofthegods.com/magnetic%20amplifiers.pdf
first link didnt work 

I have done some testing of a variation of the bi toroid transformer.
Insted of cutting down the size of the primary magnetic circuit I thought maybe I can use magnets to increase the reluctance of the primary circuit and direct the flux through the two secondaries.
Here are some pics and my results.
                   

You need to add alternate path between secondaries so that they go pass the primary. This way your secondaries will amplify each other. You can also make it 3d: stack I cores between two toroids. Your coils all in I-cores, one is primary and rest are secondaries. Flux from primary is divided between each secondary, but also each secondary amplifies rest of secondaries. Maybe better  to put primary in the center, then couple it to one secondary that is in toroid, this shorted. You could also play with permeabilities, low perm in primary and higher in the secondaries.

I have gone ahead and cut the three phase transformer as pictured above.
Initial tests ara e bit puzzling.
The Transformer is wound for 480 volt star on the primaries 30 volt delta on the secondaries.
I have cut all the connections so I have 3 independent high voltage coils on top of 3 independent low voltage coils.
I am running 240 volt in to the primary in BITT configuration as pictured above.
On the 2 secondaries I measure 46 volts with no loads.
With 0 loads the supply is 240 volt 108 ma
With 1 load the supply is 240 volt 127 ma
with 2 loads the supply is 240 volt 107 ma
With the loads on both secondaries I have 89 volt and 13.5 ma on EACH secondary coil across a light bulb
I am not sure what all this means.
Maybe I need higher voltage in the supply to saturate the primary circuit more. 
But when I put the cuts in the primary magnetic circuit the no load current from the supply jumped from 53ma to 150 ma.
Not sure where to from here

When you made cuts, you reduced the flux path through the primary. This means self inductance of the primary went down and it now allowed more current to pass.OK I follow this At the same time, this reduced flux is seen also in your secondaries and since it is now reduced, it creates less power there.Not sure I follow here. If more current passes in the primary then more ampere turns therefore more flux ?
 
Take a look at how small trafos work. Primary coil is very fine wire and coil easily has over 10000 turns. They can be connected directly to mains as their self inductance is so high that only little current goes through. Just enough to create little flux in the core. If two such coils are connected in series as primary, then no current gets through and secondary cannot get any power out. This I have tested.
 
What you need to next is to add more turns in all of your coils. More turns the better. Maybe time to smash couple of trafos and get your fine grained coils from there for quick prototyping. Chinese trafos are good, typically their E cores are not welded shut.
 
You should also experiment with shorted secondaries. Short one secondary coil to get maximum output from the second secondary.Tried this today see below

 
Because my transformer is a 3 phase 480 to 30 volt there are 2 coils on each leg
So I connected the coils on each leg together in series to get more turns.
 
Tests with coils on each leg in series input in milli amps
1. No load = 105
2. one load = 109
3. two loads = 106
 
I then cut the cuts deeper to make the reluctance higher in the secondary
1. No load =157
2 one load = 160
3. two loads = 156
4. middle leg shorted one load on end leg = 165
5. middle leg shorted two loads on end leg = 168
 
Then I cut the cuts deper again and put the no load amps above 200 ma which is my meter cutout so I cant get fine resolution readings now cause I have to go to the higher range.
 
I had my capacitor box on the bench so I thought to try it in paralell with the primary core.
I hooked it up ans started engaging the caps one by one with both secondaries loaded.
the input dripped to 60 ma like it was before I cut the core but the effect of the primary amp drop when connecting the two loads completely disapeared? not sure why or what it means.
I suspect it is playing with the power factor and changing something.
I would like to run the primary in resonance if anyone knows a circuit to run a transformer primary in resonance.