I didn't have time to read all 19 pages, but if she just started laying on April 23, you still have time. I prefer to not bother them too much the first few days. My choice of last resort is aspiration. But it usually takes at least a week, often 2 weeks or more, before the eggs harden and you lose that option.
Here is the order I usually proceed when I suspect egg binding:
First, leave her alone, making sure the nest box is fairly full of fluffy, damp, moss.
If it has been at least 48 hours since the last egg was laid, some gentle exercise climbing, or swimming in warm (make sure it is not too hot!) water may help.
Give that option 24 hours to work. If not, and there is an egg within an inch or two of the cloaca, I try gentle massage, but only with a lubricated probe inserted first (gently go around and around the cloaca, and it will gape open), in contact with the egg, to make sure it is not pushing the oviduct out in front of it (see pages 127 and 138 in my book for details). If you get one out, wait until the next day to see if the next one has been laid or is in position to guide out, too.
If that doesn't work, you can try to aspirate the most distal egg as I describe in the same section of my book. Don't get too aggressive too quickly. You could do more harm than good.
Good luck!