802.11b use with 2.4ghz (fhss) cordless phones

I'm aware of the unavoidable interference between 2.4ghz fhss cordless
phones and 802.11b networks, of which I have first hand knowledge.
Using the phone knocks down/out my 802.11b network.

I'm not an engineer, but I'm wondering if the following idea would
work - put a low-pass filter between the cordless phone base unit and
the antennas, filtering out the high end of the 2.4ghz band, then use
channel 11 on the 802.11b network. I think that the bandwiths of the
fhss frequencies are very small (on the order of 1 mhz) so only a very
small portion of the 2.4ghz band would have to be filtered out to
eliminate interference to channel 11 of the 802.11b network.

Here are some possible problems that I intuitively feel might be a
problem.

1) The 2.4ghz phones will not work or will work badly if they can't
use the upper frequencies of the 2.4ghz band
2) The handset will still be using the upper part of the band and will
still provide interference.
3) The frequency of the beacon signal on the 802.11b network - if this
is affected regardless of which channel is used for communication,
might this still cause the network to crash? I don't know much about
the beacon signal of the 802.11x network

My limited knowledge of fhss is that it is a protocol that, among
other things, is meant to limit interference so that maybe the absence
of certain frequencies would just be interpreted as interference on
those frequencies and that would result in using the available
frequencies only, eliminating the interference between the cordless
unit and the 802.11b network using channel 11.

I know that switching to 802.11a or 5.8ghz/900mhz phones would work,
but the filters might be a lot cheaper (?) - and a fun project to
boot.

Any engineers/radio enthusiasts out there have any idea if this might
work?