Extend range of unencrypted WLAN of third party router *without* using WDS

Question

Hello,
Imagine the following scenario for which I would like to find a solution -- but I think it's impossible, so I'm looking for hints:
My neighbour operates an open (unencrypted, unprotected) wireless network that I can use. He uses a third party WLAN router that does not support WDS. I have good reception only in a certain area in our house, so I would like to extend the range of the network, using my Airport Express station (or possibly other hardware).
I cannot make changes to the configuration of my neighbours router anyway, because we don't know the password for the configuration pages (and we don't want to reset the device to factory defaults).
I know that normally one would configure the two routers (his and mine) to use WDS (each knows the other's MAC address, uses the same channel, SSID and encryption setting etc.), but this is not possible here.
I could join his network with my powerbook wirelessly and then set up sharing preferences on the powerbook such that the WLAN internet connection would be shared onto the ethernet port to which I would connect my Airport Express station to allow wireless access by other machines. This isn't the cleanest setup because I think my powerbook would have to distribute IP addresses using DHCP and NAT which my neighbour's router does, too, so we should not use the same IP range (e.g. would use 192.168.1.xxx and I would use 10.0.1.xxx) and probably we shouldn't use the same SSID, either.
Because there's no WDS support, something like the above seems to be the only solution to me, namely: I would have to join his network as a normal client and the redistribute more or less separately (different subnet/different SSID/different IP address range/...).
Now, the Airport Express can join an existing network as a client, but despite the displayed settings in Airport Admin Utility, bridging to the ehternet port or Airport Express does not work. I have read a lot of Apple documentation, and my understanding is that when setting up Airport Express to join an existing wireless network, the only purpose would be to use it as the receiving end for iTunes music streaming and possibly to connect a printer to it; but the ethernet is completely disabled. (It took me hours to figure this out because the Admin utility clearly suggests that the station would operate as WLAN-ethernet bridge in this setting, but it doesn't.)
So do you have any other solutions to this problem? WOuld an AIrport Extreme station be capable of doing this?
I don't want to use my powerbook as the 'bridge' to share the WLAN connection to the ethernet port as described above because that would require my powerbook to be on alll the time and be located in an inconvenient place.
Thanks for your replies!
P.S.: I do have some older/other wireless routers available, but I think they're not going to help because they won't allow this rather unusual setting. They're all very basic.
Powerbook G4 1 GHz   Mac OS X (10.4.7)   Airport Express

Answer 1

WOuld an AIrport Extreme station be capable of doing this?
No. The only way an AirPort Extreme base station (AEBS) can wirelessly join a network is using WDS. It does not offer the wireless client mode like the AirPort Express (AX).
Using your PowerBook as you suggested is the only solution using Apple's devices.
There may be 3rd party repeaters that you can use but I have no experience with them.