Transformer won't work for US plug
Wrong adapter
Your problem is basically entirely that you have the wrong adapter.  Your transformer is a UK worksite transformer that outputs two 55V legs with an inaccessible center-tap for the grounded neutral, and thus uses IEC 60309 pin and sleeve (also known as &quot;CEEform&quot; or &quot;Commando&quot; in the UK) type connectors as they are rugged and weather-resistant.  These are not intended to mate with the Schuko plug on your current adapter, though, so you'll need to get or fabricate (using a short length of appropriate cordage as a go-between) an adapter from the appropriate pin-and-sleeve plug to a NEMA 5-15 cord cap and use that instead.