Does a WAP supporting WPA imply it supports EAP standalone also? (e.g. BEFW11S4 v4)

Here is my situation: I have a BEFW11S4 which is currently acting as
my NAT firewall and my LAN switch for three hardwired PCs. The
BEFW11S4 is also my WAP for one wirelessly connected laptop (a
Thinkpad T40 with a built-in Cisco Wireless LAN Adapter - 350 series I
think which is 802.11b only). I am preparing to add another switch
(hardwired to the first) to support a couple of new PCs in another
area of my home which is located remotely from the first switch. In
adding the switch, I would also like to improve my wireless security a
bit. My BEFW11S4 (first generation) has only WEP, and from what I can
tell from this forum and the Linksys web site, no firmware upgrade
will improve that. Thus, I was thinking of adding a BEFW11S4 v4 as it
appears that can be firmware upgraded to support WPA. However, my
laptop client card can only support 802.1x (EAP) and LEAP, and it
cannot support full WPA even with the latest firmware update. My
questions are:

Does a WAP that supports WPA imply that it supports EAP standalone
also? If I understand the technology correctly, WPA requires EAP
internally as part of its operation, but in reading through the WRT54G
users guide (which I used as a best guess as to how the BEFW11S4 v4
would work for WPA), they suggest that one can set WEP, or WPA, but
not EAP alone. Thus, since my client card only supports EAP, my only
compatible mode with BEFW11S4 v4 seems to be just WEP (which does not
provide me any benefit). Another WAP, the WRV54G, includes
configuration instructions that suggest it can support EAP standalone.
Thus, it seems I am out of luck in wanting to get EAP only function
from the BEFW11S4. Is this correct?

Are there other products similar to the BEFW11S4 which would allow me
improve my wireless security in this case? The WRV54G is much too
expensive for this application.

Thanks for any advice and insight.

Jim