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You might want to think about a smaller BTU ac. We put a Coleman polar cub 9600 btu unit. It is stand alone with internal thermostat. It does a great job. Both units run well on 30 amp hook ups even on the hot days. It cools down the bedroom very well. One other consideration is the location of your thermonstat for the rear ac. If it is on the steps to the bedroom, the second ac will compete with the setting on the rear ac. It just takes some monitoring to resolve the issue.
Hope it works out for you.
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