My first thought was just to put a string parallel to the front edge of the head tube, and mark where it hits the floor. There are a couple of chances for making a large error with this though:
-Lining up the string is similar to winding sticks used in carpentry, it takes some practice to look at the sticks square on so that there is no parallax error. Because the string would need to be out 3 inches to clear the fork, the chance for error would be worse.
-The string would be at the edge, not the center line of the steering shaft, and when it hits the floor the difference would need to be subtracted. Since it hits at an angle, the chance of error increases.
I decided to use the center line from the start, and attach little right angle squares sticking out for lining up the string. To find the center line, I took a piece of cereal box, and cut a slot in it that just fit over the head tube:
Then tape this onto a yardstick so that it sticks out square (perpendicular) to the side. Mark the center of the slot on the masking tape on both sides of the yardstick (so that you can flip it over for left and right sides). Then put pieces of tape at the top and bottom of the head tube on both left and right sides. Slide the slot over these pieces of tape while holding the yardstick against the seat tube (this keeps everything lined up square), and use the slot center marks to mark the center line on all four pieces of tape.
The left end of the yardstick is resting on the seat tube, to keep everything lined up square.
Do this on both left and right sides to get the center line at the top and bottom of the head tube.
I decided that holding two little squares on the center line marks while lining up a string was too hard, so I made a jig that could be clamped on the frame. First I cut a cereal box template that lined up with the center line marks, and ran back along the frame 10 inches. It's symmetrical so that it can be flipped over for the other side, and I had to cut a notch in it for the shifter cable ferrule. I traced this onto a piece of plywood and cut it out. Then I cut a board, that was wide enough to stick out past the fork sides, to be as long as would fit above the top of the fork (the inside corner had to be angled to clear the steering bearings). Glue them together, making sure they are square:
Cereal box template, finished jig, and square used while gluing the boards together.
The jig clamped on to the bike, lined up with the center marks on the head tube.
The board sticks out far enough to clear the forks, and it turned out so solid for taking measurements that I used a yardstick resting on it, instead of a string. Here is the basic setup for measuring:
Note: This is on a level, flat floor, and the bike is propped standing straight up.
(The cereal box on the yardstick near the brakes is from marking the center lines earlier, and is not part of this step.)
I've used a screen door spring going back to the crank to hold the wheel straight, a bungee cord would also work. You need to measure both sides because the wheel will almost always be resting turned a few degrees left or right, and taking the average of both sides removes this error.
Rest the yardstick on the center line board, let it slide down slowly to hit the floor, and mark the spot on masking tape stuck to the floor. Hold up a level that lines up with the center of the axle, and mark where it hits the floor. Measure between the two marks, repeat on other side, and calculate the average to get the trail.
One other thing you can measure while the yardstick is set up is the fork offset:
The bottom edge of the yardstick is on the fork stem centerline, and the distance from there to the center of the axle is 1 3/8", or 35 mm fork offset. Again, use the average of both sides.
With a little care this method should get you pretty good results. It can be improved by watching the details, such as adding a shim to keep things square if the head tube is not the same diameter as the seat/down/top tubes. The head bearings need to be in good adjustment too. On a bike without a round head tube you might have to use the bearings or handle bar stem instead. It might also be possible to make the jig out of foam core artist's board and hot melt glue so that you don't have to do wood working, but clamping it to the frame will need extra TLC and shims to avoid squashing the foam.
Getting back to this bike's measurements:
-Stock, the crank center line is 11 3/4 inch off the ground, head angle is 68.5 degrees, and trail is 3 5/8 inch.
-With the pedals dropped to a crank centerline of 10 1/4", the head angle is 64.7, and trail is 4 7/16".
Dropping the pedals will put the bike on the slow side of the recommendations I've collected. I could cut the head tube tube off the down tube and reweld it back on steeper, but I think I'll leave it as is. It isn't as extreme as many choppers, and I actually desire slower handling. When riding along after 25 miles, I don't want the bike to dart left in front of a car if I scratch my back, the emphasis is on going straight. The extra trail will also make it correct it's path a little more if it gets bumped sideways by road garbage when I'm tired. The cargo bike will have a long wheelbase (which is slower), and is heavier (slow handling again), so I may be pushing my luck by adding slower steering, but this can be an experiment, it will be good to find out how much of a difference it makes.