The wording is clear, but the intent is not because it doesn't make any sense that the 2nd veil grants a +2 bonus while the 3rd, 4th, etc, veils add a +1 bonus. That's the problem. Each additional veil should add the same bonus, so the DM doesn't have to question what the designer is thinking.
I don't see that there's any difference in how much sense it makes in either case. We've had similar SA in the CC that go both ways. For example, the
Saluqi's Pack Overrun uses a bonus equal to the number of monsters (like the version I favour), while the
Pack Spider's Swarmfighting uses a bonus equal to the number of
additional monsters (like you appear to prefer).
It all comes down to taste in the end, and I fear it might be a long while before either of our tastes change!
What we really need is a third party to arbitrarily apply their taste to break the deadlock (assuming they don't fancy a 3rd option to make this debate even more protracted

).
If you don't want to be constrained by Aid Another, let's just say that the "bonus" for the first veil is already in the DC we stated for a single veil, so it is +1 per additional veil.
So, just to be clear, when you say you want to include the "bonus" for the first veil you still want the DCs to go 18, 19, 20, 21, 22, 23, 24 from the first to seventh veils, you're not wanting a +1 for the first veil and have the DCs go 19, 20, 21, 22, 23, 24, 25?
In either case, am I right in thinking you want a "multiveil" paragraph worded something like:
If the opponent is entangled in more than one veil, the enemy only needs to make a single Escape Artist or Strength check to escape, but the DC to escape is increased by +1 per additional veil.