Is it possible to overcome a transistor's current limit by running it at lower voltage?
Not only can't you do that, but very likely you can't run it with 800 mA and 5 V at the same time either. 

Typically the voltage rating is the maximum voltage the transistor is guaranteed to block in the cut-off state. 

And the current rating is the maximum current in a fully saturated state (BJTs) or in the triode region (MOSFETs).

When operating in the forward active region (BJTs) or saturation region (MOSFETs), the maximum power limit is likely to give a lower limit on current &amp; voltage than either of those limits.