"it would mess up the mounting of the exhaust and weight distribution."
Most exhausts have enough flexibility to cope with the movement, it is after all a common feature of karting that one has to change the gearing.
Moving the engine (17 kg) the less than 1 centimetre needed to take up the change in chain length isn't enough to seriously affect your weight distribution. In its helmet your head weighs half the engine, and it moves far more than 2 centimetres forward and backward as you drive. Yes, getting the distribution right will help enormously in getting the driving right, but consider that the limits are normally quoted as 55-60% to the rear (the exact setting will depend on you and the kart).
If one assumes that on a 60/40 balance, a 160kg kart and driver and a 1040mm wheel base then the 'weight' on the back is 60/100*160*1040 KGmm=99840 kgmm
moving the 17kg engine forward 10mm is a change of: (170*10/99840)*100 =0.17%
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