I have had java moss and taiwan moss. They look very similar but the in comparing the two, java moss does not stay as green and thick as the taiwan moss. When I had java moss, I was disappointed that it didn't stay nice and green, so I got the taiwan moss.
For your java moss, you may be able to help it along a bit. Your lighting looks fine. A 20 gallon long is not too high, so your lighting should be able to penetrate down to the bottom. Just in case it isn't getting enough light down there, try moving it up closer to the light if you can. You could maybe get some driftwood that is taller and attach the moss to the driftwood where it would be closer to the light. My moss is at the top of my tank.
Also check your nitrates. Are you adding any fertilizers? If your nitrates bottom out, you would definitely see an algae outbreak, but even these low-light plants consume nitrate enough that you may have to supplement. Your fish bio-load doesn't look high, so I would suspect that maybe your nitrates are low. You want a level of 10-20 ppm
At one time, I had a 5 gallon tank with one betta, some fake plants, and some java moss. That one clump of java moss in the 5 gallon tank consumed all the nitrates and when I tested, my nitrates were 0. So even though you said the other plants were growing fast, I would check the nitrate level.
You can also pick out the brown pieces in the moss and spread it out a little so that more of the little branches reach the light.