I cannot answer your question, but I can provide some advice. We also enclosed our lanai, and went to add AC. I ended up contacting an Engineering company to produce a ~20 page report for the county at a cost of $250. The report gave me the exact size of the AC required, however, I came up with the exact same number when i was researching mini-split systems, several of the sites have a way to fill in the room info to get the size requirements. As to whether this will strain your existing system I have no idea. I am going to send you a PM also.
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Pennsylvania, for 60+ years, most recently, Allentown, now TV. 
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