How do overwintered onions decide they are ready?

I think onions will only grow up until mid summer irrespective of what size they get to. It sounds like it's the shade that's the problem as onions like full sun and whenever mine get shaded by other plants they are always a lot smaller.

Onions grow leaves while the days are lengthening, i.e. until mid-Summers day, then they change to growing a bulb. Whatever size your onion plants have reached by mid-Summers day will largely determine how big their bulb can grow. Hence the reason why competition growers sow seed early in January.

There appear to be 3 types of onions, not varieties.
These are:

Short-day onions: These start forming bulbs when days are 11-12 hours long.
Intermediate-day onions: These need days that are 12-14 hours long.
Long-day onions: These varieties need days longer than 14 hours.

So it depends on what type your variety falls into.
I will say that I have never seen any variety classified by their type.

The site this came from is:
http://www.vegetableexpert.co.uk/GrowingOnions.html

It further states:
Bulb formation is affected by temperature, light intensity, and the amount of light and darkness. Once the balance of daylight and darkness reaches a certain point, leaf growth ceases and bulb growth begins. Onions are classified as short-day, intermediate-day and long-day:

It's important to choose the right type of onion for your area. Pick the wrong variety and you'll still get onions, but they probably won't be as big as you'd like. In general, long-day onions grow better in northern climates and short-day onions are better suited to southern gardens. Intermediate or day-neutral onions will grow anywhere. Growing short-day varieties in the North will result in leaf growth stopping too soon to produce a large bulb.

I read it a couple of years back and when I plant onions I often wonder what type they are and am I sticking the right type in the ground. Basically not a clue

Have no idea which varieties fall into which classification, but it might explain why a variety grows fine for one person and not so well for another. Especially if someone is in the north where length of day varies most.

Unfortunately I don't think you'll ever have much success growing onions in a shady spot.
You really need full sunshine otherwise you'll just get loads of tops and no bulbs.
Don't add too much Chicken Poo as this is very high in Nitrogen and you'll get a load of thick necks and small bulbs,.
Sturon are a good variety though as are Setton.