I compared an out of the box form with connected webparts with a custom form to see the difference. I noticed two lines of code encapsulating the webpart connections so I decided to copy just those lines (omitting the connections since they will not apply on the custom form) and pasted them into the new form, inside the table and just before SPDataSource if you have one. Example below. Code in question is highlighted.
<table class="ms-core-tableNoSpace" id="onetIDListForm">
<WebPartPages:SPProxyWebPartManager runat="server" ID="__ProxyWebPartManagerForConnections__">
<WebPartPages:DataFormWebPart runat="server" ......
Once the code was in place,
Correction, I was only able to establish the connection between webparts using SharePoint Designer. The web interface still reported "No Provider Schema" error. Hmm...
This solution has only been tested with SharePoint 2013. I assume it would be the same for 2010 however I cannot guess about 2007.