Sorry for the delay Jerommel , the winter came back here and I had to clean my yard...Now, I'm back in business ...
I respect your decision , the new toroid should do , just keep an eye on the heating...
About the diodes , I see that you do not want to stack its. Good call , I'm not doing like this either , but in some cases I had to do that ( no space at all ).
The Schottky diode : SK 86 ( Diotec Semiconductor ) should do the trick . I'm using this diode for few years now , and never failed on me.Is a little bigger than ss54.
The next diode , from the link :PDS1040-13 Datasheet(PDF) - Diodes Incorporated , ( just click on the image on the upper , left corner ) , 10 Amps , are the best I ever used ,and most of its were recovered from power supplies ! Even Fenix are using these for their TK 75 ! This one is easy to mount , regardless the distance between the board traces ,cause of the katode that is used as a heat sink , and the height of it , less than 1 mm ! I'll choose this one...
On the FET side , here the possibilities are almost endless...Is all about if me , or somebody else, ever used some in their modding attempts. I hope that at least few more guys to chime in , with their experience...COME ON BLF MEMBERS , THIS THREAD WILL BE , LATER , YOUR GUIDE IN MODDING THE HAIKELITE HT03II !!!... What I used and had good results are the following :
The old 436 :aod436_Rev4_rohs.xls - aod436.pdf , this one is a "mule" , reliable and with good parameters.The order of the pins are the same like the ones from your board :gate , drain , source , from left to right .Is a little bigger , but can be soldered in the space.
TPCA8028-H Toshiba Semiconductor, TPCA8028-H Datasheet , smaller , odd terminals (as a IC) , reversed order :123 pins=source , 4 pin=gate , 5678 pins=drain
Excellent Rds on , great power dissipation with no heat sink ( 1.6 - 2.8 W) . Used it in a buck driver LX-9028, 12.6V ,3X XM-L2 serie , current 4.5 Amps , working as a dream...
PH2925U N-channel TrenchMOS ultra low level FET - PH2925U.pdf , suitable for drivers with 2S batteries , not for single cell drivers (the threshold gate voltage a little high ) , very reliable , good dissipation capabilities .Reversed pin order , but not a problem , just flip it.
These are the ones that I used in more than one tests. For sure there are a lot more , but I do not know , or test ...
I do have a strong suggestion , based on my trials and errors ( A LOT OF ERRORS... MORE THAN SUCCESS !!!) . Do all the test on ONLY one channel , and after you got the best result ,operate the other 2 . The resistor mod should be the last one , because , most of the time , due to the spreading of components parameters ,you will have differences in led's current , that can be equalized thru resistor mod.
Good luck , just wait to hear from you...