I skipped the designer and created a custom aspx file with my own HTML fields, and I used JavaScript to build a WebLink search URL.
Basically, I capture the search parameters with my fields, then create my own URL based on the search URL syntax and open it in a new window when they click my Search button.
To handle login, I added the aspx header from one of the built-in pages at the very top before the doctype tag.
<%--<%@ Register TagPrefix="weblink" Namespace="WebLinkControls" Assembly="WebLinkControls" %>--%>
<%@ Page Language="vb" AutoEventWireup="false" CodeBehind="Search.aspx.vb" Inherits="WebLink.Search10" %>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN" "http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
Once I had the page working, I just linked it on the Welcome page as a custom link.