Spectrum does make a difference, and especially when you are dealing with minimal lighting to begin with. However, this cuts both ways.
Studies have proven that aquatic plants in an aquarium will grow best under light having a colour wavelength between 5000K and 7000K. The "daylight" tubes work best, with a kelvin around 6500K. These are strongest in the red, blue and green wavelengths. Colour rendition of fish and plants is also true within this range. Red and blue are essential for photosynthesis; the addition of green is interesting, and Walstad suggests this may be due to the additional brightness of the light when green is included.
The problem with the so-called plant or aquarium tubes is that they are high in the red and blue but no green. The result is a sort of purplish hue. Some may like this, others don't, but more importantly is the fact that these tubes produce less intense light than the "daylight" I mentioned above.
I did a series of experiments with single tubes over my 29g tank a couple years back. With the same plants and fish, and same plant fertilizers and water changes, I found that the plants thrived under a Life-Glo tube. Under the Aqua-Glo (same size and wattage) they began to deterioriate within a few weeks. I also used a GE daylight tube and they again literally melted away. I put a new Life-Glo in the fixture, and the plants that were not completely dead revived over several weeks. Each of these tubes were over the tank for 5-6 months. There is certainly no doubt that the tube is important.
On my dual-tube tanks that take 4-foot tubes I do use the cheaper tubes. I've had good results from one Sylvania 5000K and one 6500K together, or two 6500K together. The 5000K adds a bit of "warmth" which is nice for the reds.
Two 18-inch tubes over a 4-foot tank with this depth is really pushing things. And I will guarantee that you will not have much luck unless you get either of the two tubes I mentioned previously, or something that is similar. I name these two because I have used them so I know what they will do.
Another option though is to replace the present fixture. A single T8 48-inch tube would be a slight improvement; I had this over my 55g back in the 1980's and some plants managed; again, use the Life-Glo or UltraSun tube. A dual-tube with 48-inch tubes would be much better and you could use the Sylvania or Phillips or GE tubes.
Byron.