I think we might have to pencil in the question of induction heating of asteroids as well. The young Sun can do that but I've no idea about f type stars, do they, f types, switch off that evolutionary phase earlier, or later?

Yes 1/28 it was I think . 4% gives for Jupiter sized planets about 40 bodies.

I performed some simulations having some Jupiter sized planets around our sun in a coorbital orbit at 5.2 AU , meaning several Jupiters in the same orbit , but separated by fi. 60° in their orbit .  
To my surprise I don't get stable orbits with a lot of Jupiters , except for the case in which I put an extra Jupiter in the L4 and the L5 lagrangian point , thus creating trojans the mass of Jupiter itself .  
 
So , returning to the Original Post of Bob : trojans may partially explain the big dips observed . I tried to introduce large trojans in order to simulate the big dips observed , but there seems to be a limit of the number of large bodies  
 

Thanks for the info Tony  
I've also found this :  
http://www.math.cornell.edu/~templier/junior/final_paper/Thomas_Greenspan-Stabil ity_of_Lagrange_points.pdf
pointing to a ratio m1/m2 > 24.9 , which is indeed 4%  
After restoring the broken links the equilateral 2 planet configuaration is analysed here :  
http://iopscience.iop.org/article/10.1086/341173/pdf;jsessionid=EDB1DB457C20A295 660CC4118B3F296E.c2.iopscience.cld.iop.org
indeed pointing out to a value of mplanets/Msun = 0.03812

I had hoped that that guy Anders Sandberg, might have joined here, as he does seem to know his stuff. Early days,he miht just be slow at reading his blog replies.

Here's the result of my best simulation I can come up with in the case of Trojans :  
 
Suppose the light curve of the planet is due to a transit of  major Jovian Planet , followed by some Trojans , as depicted in the picture hereby .
I "played" with some initial settings of the system ( coorbitals) and limited myself to  a trailing and a leading Jovian planet of the same mass as the primary .      
In the setup the following system is stable : A Jovian planet at 5.2 AU , having 0.4% Solar mass ( NOT 4% !) , followed by a trojan of equal mass at 60° and behind a trojan of equal mass at 60° . So total mass of all bodies being 1.2% of the solar mass.  
Replace the trojans by some bunch of smaller bodies , and maybe we get the light curve observed ?  
( I wished I had come up with a bigger ratio of Jovian Mass to Solar Mass , but this seems not to be stable ) ...

As a demonstration of a potential Trojan System around the mysterious star :  
 
http://orbitsimulator.com/gravitySimulatorCloud/simulations/1446914152802_Jupite r%20Trojan.html
 
Simulation consists of :  
- the central star 1.43 Ms
- two Jupiter planets , having each 5 MJup ,  at 6AU distance , sharing one orbit .
- one of them has 7 Earth sized moons around it .  
 
The systeem seems to be stable .  
Edit : link above doesn't seem to work ; I'm pretty sure I posted it with the Save feature , also providing some description  . Can't find the sim either in the list of simulations.

Thanks . I was worried not to see the sim in the list and configured the sim twice . Now I see I have to refresh my browser in order to see changes.  
Both are there . You can delete one of them if you want.