Usually people consider the extras to be expendable. Pull or cut them to thin out.

There are some who do transplant to keep the extras. It's good and useful but even with extras, you probably only want a few extras, and the remaining still have to be lost.

This is until you get a better feel for the germination rate of a particular seed or brand, and can save some seeds/plants by not planting them.

The peas

The peas look fine and shouldn't need any thinning.
The Kale is also fine if you want baby kale for salads, etc.
If you want full sized kale plants you can thin to 8-16 inches (depends on you, I use 16 for big plants). And if you want to save the thinnings, i'd do it now when the plants are small. Dig them carefully, damaging as few roots as possible and replant them into small pots with good potting soil. This way you can take better care of them for a few weeks till they recover. Then you can transplant them into another bed at your desired spacing.

-Mark

Would it severely damage the seedlings if I just planted them into the soil without having them go through "recovery?" Taking care not to damage the stems or roots of course in the process...

Yes, you certainly can give it a shot. The success rate will depend on how much stress they go through. This includes many factors like plant/root damage, soil conditions, weather.
Be sure to keep them well watered after transplant and good luck.

-Mark

Ok! Will take that info to mind.

As madroneb said the peas don't need thinning. They are already at a good spacing. The kale will transplant fine straight into a new row if you water it well on replanting. It may stall a little but that doesn't matter because it will help stagger the harvest and reduce the chances of a glut. Again as madroneb said, if you lose interest in transplanting so many seedlings the excess kale sprouts will go well in salad. And you now know not to sow so many brassica seeds next year! They germinate really easily.

You never reported on how things went last year with the wood's loam on top of the lawn. Is that what is in the photos?

Pnbrown, sorry, I've completely forgotten! Yes that is whats pictured. I limed last year and apply wood ash every now and then. I also take composting very seriously!

And the spacing of the peas may seem good in the pic, but honestly I don't see how they could possibly grow with so little space!

Will post garden and soil pics later on...

Oh, and I didn't apply soil directly over the grass, pnbrown.

honestly the peas don't need more room, I space mine only about 2 inches apart. They will need a trellis to climb up though.

Yes - peas have a really low yield per plant. You need a large number to get a reasonable crop. I also sow 2 inches apart each way in bands about 6 inches wide. Twiggy prunings will work as trellis. Like this (note this is a very threadbare row - a lot of seeds were lost to mice):

Indeed peas are famous for tolerating high density. I generally do a double-row in at least a 3-foot wide space, so there is plenty of room for the pea roots to the sides.

The easiest way to transplant seedlings is right into a bowl. I consider "thinning's salad" a delicacy, course I have dr it up and make it fancy for other people, or else they think it's just scraps or something.

Wow, I never knew peas needed so little space. So I'll only thin the peas that are literally growing right on the same spot! I don't really like the idea of eating seedling greens though...

Pea sprouts are delicious. If you do need to thin make a salad or stir fry with the peas and micro-kale.

Still, the idea of eating seedlings is not attractive to me... So I'll transplant this Sunday before the rain.