I just arrived in MLE today and because I will be doing a quick turnaround here later in the year, I checked my options.

There IS a "transit passenger" exit before immigration. Once you enter the building from the tarmac, just turn left immediately.

Even if that wouldn't work, immigration was quick, even when arriving after a seemimgly full UL flight today. 15 min tops from leaving the bus to arrivals hall. You could then turn left and go straight to departures again.