The judge also has to certify any class action settlement. And any member of the class may file an objection stating that the terms of the settlement are unfair. The judge reviews the objections (including to attorneys fees) and can reject them if the settlement is not reasonable for the class. On top of that, you do have to notify members of the class (by publication if they aren't individually known) of the terms of the settlement and give them instructions for filing objections before the settlement will be approved.
This isn't to say that no class action is ever settled on terms unfair to the class, but there are a lot of protections to prevent that, and overall class actions are a valuable tool to protect consumers. That's why companies are increasingly trying to remove your right to join class actions by hiding terms forbidding it in EULAs and other fine print agreements.
I wonder if this problem would improve if judgments always expressed an amount per member of the class, rather than a total amount?
Believe me, class action plaintiff attorneys are not falling victim to any psychological quirk that makes them underestimate what the size of the verdict should be. They get paid based on the size of the verdict and are therefore fully adept at imagining every reason why the verdict should be very large. They make these arguments quite clear to the court, and as you say it's frequently by attempting to couch the verdict in terms of benefit per member of the class.
The real reason for small awards is that most of these large cases end in settlements, not verdicts. And plaintiffs have an incentive to settle for much less than the full value of their claim. This is because there is risk (usually quite a lot) in taking a case to trial, so you must discount your expected verdict by the risk you will lose at trial and get nothing.
In addition, it's very hard to prove damage in class actions. You need to show that all members of the class (or at least large groups) suffered very similar damage. If damages vary by individual, then individual proof is required (this makes sense, part of a case is proving your damages) and you will lose your right to proceed as a class action. If that happens, it's basically like coming away with no money, so plaintiff lawyers can't always claim every dollar that might be on the table. They stick to the claims that they can apply on a class-wide (or close) basis.
Ultimately settlements are about taking a sure deal for less money rather than taking a risk to try to get the full amount you believe you are entitled to. That's the way settlements work, and that's often a good deal for the class.
[EDIT] Personally this has resulted in a philosophical challenge because I was under the impression churches were being given a free ride by not paying taxes; this is not the case. They have a constitutional right to not pay taxes.
Is this clever trick possibly accessible to average citizens, though? Is it possible to, say, all join a massive corp. so that our actions are protected us from lawsuits from corporations?
I've observed that class action lawsuits usually benefit the defendant greatly in that the nature of class action suits is that they deprive any persons with standing from all future legal actions on a matter. Sometimes they get nothing as part of a settlement, other parts they receive some token coupon that usually has restrictions to make it useless. In no case is the opinion of the members of the class taken into consideration, nor do they have any right to object to settlements, nor are they normally informed of the settlement until after it has taken place.
In effect, it's a similar protection scheme to how Congress passed a law banning the filing of lawsuits against BP in return for them paying a fine for oil spillage that is vastly below the cost of fixing the damage.
Many actions that are labelled as "settlements" or "fines" are actually bribes paid to the legal system in return for total immunity from future lawsuits.