Your analysis doesn't make sense at all. When you install the stern kit, it comes with a vol control. The bigger speakers require more power to drive them. Therefore, you turn the system volume up. I usually go to around 48. Then you turn the vol control knob that you just installed down until the speakers are the right volume you want. This results in booming bass but normal volume speakers.
The vol knob will lower the vol of tgd backbox speakers. If this is not what's happening then you have it installed wrong.
What part of what I described is different for you?
Also the Tz kit would be totally different and incompatible. The speaker in a WMS system is crossed over way higher than the stern subs. In addition the older WMS sound systems had only one audio amp. Therefore the vol knob is on the sub. Wpc dcs, wpc 95, Sega, data east, and stern all have two amps. One for back box and one for cabinet (sub).