There is a world of difference between the A340-200/300 and the A340-500/600. The smaller aircraft, even with the C4 engines, is far from overpowered! The 346 on two is probably not far short of the B777 on one, which gives an idea of the increased performance of the newer aircraft - and it's over 100 tonnes heavier than the 'little' one! Those non-pilots reading this should bear in mind that, because of our route structure, we are nearly always operating close to our maximum take-off weight, unlike short-haul 757s!
VAA, at LHR, always accelerates at 1500' AAL to 250kts/min safe, as per the published procedures. Even in a C2- powered A343, this technique will nearly always achieve the published minimum climb gradients up to 4000', so I've no idea why WAWN's company climbs at V2+10 to 4000'. This may be the very problem (and company) that Cartman's Twin is referring to. On the very rare occasions when the C2 A343 can't make the gradient at 250kts, we limit the acceleration to 190kts until the kit confirms that the constraints can be met, as Spocla says. This normally means accelerating to 250 at around 2800ft - and we would normally tell ATC if a late acceleration is required.
Once the 250kt speed restriction is lifted by ATC, and we are sure we'll make both the SID track and climb requirements, we accelerate to our normal climb speed - approx 300 in the A343, or 320 in the A346.
As for famils, I have carried at least 3 Swanwick ATCOs on flights in the last two or three months, so they are definitely back on - and on the 340 (and we don't do anything other than long haul)!