First of all, there will be more than 1000' between the lowest available flight level and the highest available altitude if you have a low QNH. For example, in Australia, with a transition altitude of 10,000', FL110 is not available if the QNH is below 1013, FL120 is not available with a QNH below 980. This is to ensure that there is always adequate vertical separation between aircraft at flight levels and aircraft on QNH.
In your scenario with a QNH of 993 there's only 400' between FL060 and A050, a more likely scenario is if you were at FL070 and given A050, then you've got 1400' to do what towser suggested. Set and arm 5000', start your descent, call "transition", change to 993, call the alert for 5000' (if that's in your SOPs), and then monitor the altitude capture.
In the aircraft I fly (Dash 8 ), if you changed to the QNH first, the autopilot will climb to maintain the indicated altitude (given a low QNH). The problem with this is that you are reducing vertical separation with opposite direction traffic that should be 1000' above you. And you will directly conflict with any VFR traffic that would normally only be 500' above you.