I have a pump with that type of smarthead. It needs more presta valve showing to work properly. It's also possible that the gasket that grabs the valve has been damaged. These gaskets can be replaced. Test your pump on a longer valve to see if the gasket is damaged.

Here's a link Valve Extender How-To - Slowtwitch.com that discuses how to use a presta valve extender. Note the remark "My two personal favorites of everything on the market are the Zipp and Shimano designs. They both feature large diameter ends with a textured surface – both essential for getting a good “bite” on most pumps. The narrow or non-textured types tend to cause the pump to slip off at pressures over 100psi (7 bar)." The BBB extenders you used fall into the category of "narrow or non-textured types."

I use pumps with smartheads of this type as a mechanic at events. I like them because they handle both shrader and presta valves. The also stand up to abuse from having the public use the pumps. I've found they have two weaknesses. You found the short valve stem weakness. The other is they don't handle Dunlop/Woods valves. I've found that presta valve extenders with large diameter textured ends handle both.