If you have the melody w/o the reverb, make a loop of it 3 times, run it through the reverb, cut the middle one and use that. It will have the end of the reverb of the first melody, which should be enough.
Even better, play the original clip once before repeating the variant with added reverb: the beginning of the music shouldn't have a reverb tail out of nowhere.
Also, verify that reverb tails are shorter than your music clip; you might need more than one repeat to reach a steady state that allows looping.
In the editing technique suggested by TheChubu, the second and third repeat in the output should be identical; alternatively, if you process with reverb one copy of the music followed by silence you can directly measure how long does the reverberated output take to decay to silence.