I have dwarf sag in 6 tanks, all with different set ups. Growth is really easy going, but the plants adapt and grow differently in different situations. There are also 2 variations of dwarf sag, one that I consider truely dwarf, and another that looks identical, but grows much taller.
Here's what I've noticed....
I have some in a tank with almost no light... that is, it gets all it's light from sunlight, and receives no direct sunlight. The plants grow super slow, and the leaves stay fairly thin, and are susceptable to algae growth... but they're steady and growing nice without ferts or added light, after 2 years. The viewing light for the tank is rarely on, but is only 7w. The leaves do stretch for light.
I have some more in the 20 gallon cork tank in my signature... and they've grown exceptionally well with 40w of light, occassional ferts, and no co2. But in the last month and a half, I've let the surface of the tank get completely overgrown, and the sag shows it's disliking by nearly doubling in size. It's as if it got used to the higher light, and still wants it, so it's getting huge to absorb more light.
Then, I have a 15 gallon breeding tank that I threw a few smaller sag in maybe 6 months ago. The tank has had a variety of lighting situations over the past 6 months, but the most consistant aspect is that the front of the tank gets strong sunlight from 2-4pm. These have stayed TINY. They're healthy, and spread like wildfire, but they stay way smaller than in my other tanks, truely looking dwarf. I like these the best, but it takes a ton of them to fill any area. I have 16 in the 15 gallon, and it looks completely empty from a distance.
So I guess what I'm saying is, dwarf sag has always been one of my favorite aquatic plants, because it's so adaptable, and I've had really good luck with it. I find what it doesn't like is when it gets too warm, and when it's disturbed. I've never found it to have special requirements. Melting could be from something other than not enough light, such as Excel dosing, high temps, or disturbed roots. The algae growth on the leaves may just be from placement... it's possible they get more light than they need right now, and the algae is taking hold... or it's possible you have another imbalance. The last thing I'd mention, is to make sure to plant them correctly. If you bury anything more than the roots, you will get melt off and eventual death. ideally, you should be able to just see the top of the root where it meets the leaves. I usually acheive this by burying it too deep and then pulling it back up a bit, or by using the roots to pull it through sand until they're buried where i like em. takes a bit of practice, but not really hard.