Yep - you're being too good to them. I would repot them into el cheapo potting soil without a fertilizer or perhaps a mixture of that and sand. They like really lean soil. Also, move them into full or mostly sun - too much shade will limit their blossoms.

Is there anything I can do to nasturtiums already in the ground to make them bloom more (and grow less)?

They are in full sun and are very leafy but no flowers yet; they germinated about 5 weeks ago.

In another bed, I have some nasturtiums that are blooming like crazy but the flowers are hidden by leaves. Is this normal, and will the flowers become less reticent as the season progresses?

This is my first year with abundantly blooming nasturtiums. Perhaps this is the secret? This spring I made a lasagna bed of coffee grounds, spruce needles, leaves, newspaper and general garden trimming junk, with a couple of inches of garden soil on top. Most of it is planted in beans,who also don't need the nutrients so much. The nasturtiums' roots must be in the still-decomposing matter below the soil, where there is not much in the way of available nutrients yet. They have small but healthy leaves and tons of flowers, all well above the foliage. They are just a cheap seed-rack variety in the standard orange. These are such pretty, easy flowers so I am pleased to have a "method" to get lots of flowers from them. Now I am emboldened to try the colors I really like, like moonlight, milkmaid and peach melba. You might try the lasagna method in a container, although the soil level will tend to sink as the stuff decomposes. Nasturtiums elongate a bit as the season progresses, though, so it might keep them looking bushier and more put-together. That is what is happening with my lasagna bed, which is in an old dresser frame.

I have had mixed experience with nasties. I'm in Z5, and typically, my yard has rich, compost-amended soil everywhere. However, I found that my nasties did best when they were put in the section of my garden that is less-nice...the richness of soil is still there, but the moisture levels are less. The area is ever-so-slightly inclined (you wouldn't notice it unless you actually stood there and looked at it closely), and the moisture doesn't retain there well.
After about 3 years of wondering why I couldn't put certain things in that area, I opted to simply allow what WILL grow there: Cosmos, Nasties, Shastas. It works.

In another area, I planted Cherries Jubilee one year in a row along the edge of a different, moisture-retaining area, and they performed well until the heat got to several of them. Most recovered a few weeks later, and I only had to pull out about 3 of the worst ones. For the record, we generally will get a heat-wave of 90+/- temps for about a week- sometimes a couple weeks- in late July or early August. So that's apparently their heat threshold.

Sorry, went a little OT there. Anyway, I also make a point of reading the packet when I buy nasturtiums, as some of them clearly state that they hold the flowers above the foliage. If it doesn't state that on the packet, I generally don't purchase them because I do like the flowers, and I'm not growing them for salads or foliage (even though nasties do put out nice foliage).

On moving them: I've only ever done it once- recently. The plants were still relatively small- about the size of your fist- and I moved two of them out to make more space. I made a point to grab a gigantic root-ball, but while I thought I had not even affected the roots, apparently the top of the plant tattled on me and told the roots that it had been moved, and it pouted for a long while. You could almost watch it falter. But I did assure it that I really wasn't trying to hurt it, and that I was only trying to give it more room out of the close-knit quarters that it was previously in, and it eventually forgave me (sometimes it helps to talk to your plants.)

Hopefully some of that info is useful for you.

I can tell you exactly what is wrong.

Many tears ago I planted nasturtiums and got lovely lush green growth but no flowers. I did some research and since then I grow nasturtiums with lots of flowers.
The results of my research---
Nasturtiums grow best in poor soil and little fertilizer. Too much Nitrogen--the first number on the fertilizer--results in lovely green leaves and no flowers.
Do not fertilize anymore and the flowers may come. Next year plant the seed and forget about them except to give them a drink now and then

I have never had trouble with nasties, until this year, planted seeds in window boxes that normally house inpatients, facing East. Results, lots of leaves, no flowers. I have not fertilized. Bummer.

Why would you plant a flower that requires sun in a shady spot? Your nasties require more than a couple of hours of morning sun. They aren't flowering because they need more sun

How do I get poor sil to plant Nasturtiums in pots?

Soil