That does sound like classic fuel pump failure now, with a full tank. There is only one electric pump, in the right hand side of the tank. There is a second outlet on the electric pump which drives a 'suction jet pump' in the left hand side of the tank to keep the fuel level balanced. The suction jet is basically a venturi powered by fuel flow.
The complete pump assembly from Audi is ~£1K which is daft, but luckily the original VDO pump is available separately here:
405-052-002-001Z for £128.
The extra outlet is the small tube next to the large pickup pipe on the bottom of the pump. This is what makes it unique to the D2:
