I am thinking that you have plenty material to make a spiderweb, if you purchase the material to make the center star. Here's my reasoning: a 12.5 in spiderweb block is made of 4 sections. Each section has 3 areas, two of which are the string portion. So at least 2/3 of the area of the block is made up of the string portion. But the string portions are larger than the star portion so I am rounding up to 3/4 to play it safe. One 12.5 block is 156.25 square inches and 3/4 of that is 117.1875, say 120 to make it easy to work with. Now that doesn't account for the seam allowances, so double it to 240 square inches per block. If you make a 4 block by 5 block lap size quilt you will need 20 blocks or 240 x 20 = 4800 square inches of string material. Now lets use your smallest size piece which I understand to be 12 by 20 inches or 240 square inches. You have 30 of them, so that would be 7200 square inches. You need 4800 square inches (a high estimate) and you have 7200 square inches (a low estimate), so I think you have enough.
Does this seem right to you?