As I mentioned in a previous comment, checking all weighings can take more than an hour on a fast machine. So I stopped trying to solve it that way, and only used it to check possible answers.
Weighing #1:
1-15 v 16-30
Excluding duplicates, this gives me the following ordered groups and possible weighings, where the number listed is the number of fewer coins (light or heavy):
15 15
------
1 1
2 2
3 3
4 4
5 5
6 6
7 7
Now, the next part was to find a suitable second weighing. I tried following the first puzzle's weighing strategy and that led to problems. I could solve everything except for 20 light / 10 heavy (see my original answer). So I abandoned that.
I tried many different weighings, and decided what I really needed to do was avoid multiples of 3 and 5. This brings me to weighing 2:
1-11 v 12-22
This gives me the following known group sizes in order and possible weighings for them:
11 4 7 8
----------
1 0 1 0
2 0 2 0
1 1 0 2
3 0 3 0
2 1 1 2
4 0 4 0
3 1 2 2
2 2 0 4
5 0 5 0
4 1 3 2
3 2 1 4
6 0 6 0
5 1 4 2
4 2 2 4
3 3 0 6
Given the general large difference between the first and third and second and fourth groups, I want to combine them for my third weighing. I tried a few different ways and came up with the following:
7-11,16-22 v 12-15,23-30
This weighing made it impossible to have many of the second group of weighings be equal, leaving me with the known group sizes and weighings of:
6 5 4 7 8
-----------
0 2 1 1 2
2 1 1 2 2
4 0 1 3 2
0 4 2 2 4
2 3 2 3 4
Now I have one weighing left, and it is:
1-6,15-22 v 7-11,23-30
This makes all the remaining weighings invalid leaving the only possibilities as 30 light/0 heavy or 0 light/30 heavy.
TL;DR
1-15 v 16-30
1-11 v 12-22
7-11,16-22 v 12-15,23-30
1-6,16-22 v 7-11,23-30