I'm not sure if my comments will help or confuse, but here goes …

I'm not intimately familiar with the LSi's, however, with regard to electronic signal theory, you may not have the problem you think you have. Here are some contributing factors:

1) The voltage needed to give 100 watts into an 8 ohm nominal load does not increase in order to provide 165 watts into a 4 ohm nominal load. While loudspeakers are non-linear, reactive loads, for an ideal linear, non-reactive load the voltage to deliver the 165 watts would actually be slightly less.

2) At mid and high frequencies, you will often find that the nominal load in both speakers is well above the 8 and 4 ohms respectively, likely minimizing the difference, in percentage, between the two.

3) Let's look at a hypothetical signal situation where a tone of 6000Hz is mixed with a tone of 100Hz. Let's say that the amplitude, not power, of the low frequency tone is 4 times greater than the high frequency tone. Let's say that the amplified signal results in 40 volts at 100Hz and mixed with the 6000Hz tone that has a 10 volt level. At times this mix will require a total of 50 volts output from the amp as the peaks of the two signals coincide, even if after the loudspeaker crossover the individual tone signals are separated. If the two tones were amplified separately, then the amp would only have to provide 40 volts for the lower tone and no more. This means that with bi-amping, the peak voltage requirement for the low frequency in this situation is 20% less. In an ideal load situation, this represents a bi-amping power requirement for the low frequency that is only 64% of the power needed without bi-amping. The high frequency power requirement is even lower for bi-amping.

But, despite all this, the bottom line is that when you set up, you will be adjusting the gain of different channels so that the sound level at your listening position does not vary from channel to channel. If, after this setup is done, you find that you have wildly varying trim levels for the bi-amped channels versus the standard channels, then you might say that more power may be needed for some channels or that some channels have much more power than needed and is not being used.