The problem with way of the burnout and bioware is the availability of a lot of useful bioware stuff: you want used muscle toner, eg. not standard (to cram in the rating 3 stuff). And, of course, the prohibitive nuyen cost which hinders you more than the essence cost to begin with.
Otherwise you want
- biocomp
- prototype
- restricted gear (adapsin)
If you want a bioware adept i'd probably forego burnout and adapsin, instead invest heavily in geneware (and drugs).
I'm relatively certain the way to do this is with Cyberlimbs and crap stats and use magic for initiative. Either Adrenaline surge and 'ware to cope with the stun or Drugs+Detox spell. Pretty sure.
Presuming your GM lets you actually use Cyberlimb stats for limits/movement/ect. Table/GM dependent on what Limbs you use for what stats and what skills, several threads floating around.
9 Agility Limbs are reasonably priced. 49,500 each. .7 Essence each w/ Biocomp. Potentially another 8 Armor for 24,000. Still have lots of capacity for whatever. If your table requires you to get a Torso and stick stats in the Torso this probably doesn't work out. (Torso and Skulls are shells and not actually Limbs so I question the RAW of putting Str/Ag upgrades in the Skull and Torso, YMMV wildly.)
The other way I can see it working is good ole Muscle Replacement 2, Reaction Enhancers 1, Narco, and Kamikaze/Betameth, (plus Detox) but you'll need decent organic stats for that. Your 'ware budget drops dramatically and you're hitting the Augmentation cap on Agility, Str, Reaction. 15+3d6 initiative and multiple capped stats seems like it would be pretty good.
