Any available wireless router or AP will allow you to set the SSID to your choosing; all will allow WEP; most will allow WPA.
For your existing Linksys WPAs, it sounds like a possible channel interference issue. You keep the SSIDs the same, and select different, non-interfering, channels for each. You also want to be absolutely up-to-date on the adapter software and firmware. Quite frankly, XP does a better job of wireless in your setting than Win2k can every do. But I understand you may not want, or cannot upgrade. Check frequently with the wireless vendor to see if newer software for the wireless adapters has been released.
For the near future: Stop purchasing APs. Purchase routers and use them as APs. They are more flexible, they offer greater firmware features, and are always cheaper than APs (for reasons that are a mystery to me).
. Since you are using Linksys, continue to do so for the near term. This allows you to use a range of firmwares -- from Linksys, Sveasoft, HyperWRT, Wolf, and several others. No other SOHO class router offers the firmware choices available for Linksys.
. Explore the use of WDS. It might be a good fit in your setting. You can do so with your Linksys APs and the purchase of WRT54G or WRT54GS and Sveasoft firmware. See: thread916-837246
. Several firmwares allow you to adjust the output power - and hence the AP density - of the AP and/or wireless Linksys router. This is a key feature in a setting in which there is overlap in the coverage zones of the APs employed. This is another good reason to continue with Linksys in the near term.
Longer Term Considerations
. The wireless field this year (2005) should see 902.11"N" standardized. MIMO enabled routers and APs will become commonplace, with or without "N" features. (You can buy the pre-"N" from D-Link now (I would not), or MIMO now from Linksys (very hot stuff). I think you are right to take short-term steps. But it would be a serious mistake at this point in time to do a site survey or make an RFP based on current wireless technology. The MIMO schema is quite impressiv in extending the range of a single Acces Point or wireless router. You likely will need fewer devices and obtain a more reliable connection with the product introductions by all wireless manufacturers this coming year.
Resources:
For all Linksys firmwares - official and 3rd party
Sveasoft firmware: