In my tests made a decade ago, I found the bleach could be of any type (copper, dichromate, ferrocianide, etc., etc.), and the print tone was mainly influenced by the 2nd developer. Methol, Amidol, Hidroxilamine (sp?), and FeEDTA give cold tones, and Phenidone, Hidroquinone, Pyro, Catechu (sp?), etc., give warm tones. Also, Bensotriazole is an effective suppresser of the warm-tone, and being added to the solution, gives cold tones even with Hidroquinone. The exact 2nd developer formula may be whatever you want (I even never measure the amounts), as the 2nd development is done in daylight. But: keep the sulfite concentration at a minimum or sulfite would dissolve some of the silver and weaken the image. Besides, it's usually better to make the developer somewhat diluted to have better control (you stop the redevelopment as soon as the tone is right, then rinse and fix your print).
Silver Chloride (as AZO) and Chlorobromide (Fortezo, Bromportrait) papers are more sensitive to the developer variations and readily change tone if you just change the 1st (and only) developer, without any bleaching+redevelopment. Silver Bromide papers (Brovira, Bromofort, Unibrom, etc.) are more stable in tone regardless of the 1st developer formula, but they too readily change the tone when bleached and redeveloped. BTW, that's why this bleach+redevelopment method way invented, as far as I know...
... I used to avoid Slavich papers back in the 1980s with all my hart. IMHO, Slavich used to be the worst photo paper manufacturer in the USSR. But now there is little choice really...