I never used the Bellini B/W reversal kit, but developed a lot of Tri-X reversal in my life.
my first guess was, that the Bellini kit includes a permanganate bleach as well, since a Dichromate bleach would be tough to sell in a lot of places.
the safety data sheet confirms this:
https://www.macodirect.de/media/pdf/32/fc/3d/BEREVBK1_Sicherheitsdatenblatt_d_4.pdf
It seems to be a pretty standard kit similar to one you could mix yourself, but cost wise it seems to me that you wouldn't save anything compared to just sending the film to Andec (the kit costing around 50euro per liter, which per data sheet would be barely enough to develop one 30meter roll of 16mm - ignoring the fact that it will be physically hard to get it submerged in 1liter).
personally I use the Kodak process but with D-19 as first and second developer. If you use a diluted paper developer instead, the only chemicals that you'd need is for the bleach and the clear batch, which are not difficult to get.
The R-10 bleach is indeed a lot less tolerant than the R-9. I found the most important thing is to do a lot of agitation in the bleach and a good wash between the baths. I also use demineralised water for the bleach and don't store it more than a couple of days, which might be over cautious, but better safe than sorry.