In your situation I would suspect that I had a lot of Nitrogen and probably not enough of the other vital plant nutrients. Even after getting a good mix of composts I was apparently short on Phosphorus last year, and my radishes and carrots did not produce the nice, big, roots that they should have. I would add either bone meal (if you want to go organic and are willing to risk giving critters an incentive to dig up your garden, or one of the synthetic phosphorus supplements). Then there is Potassium, which can be supplemented by adding wood ashes, 'greensand' (no idea what it is, it's one of those things I keep reading about from time to time (apparently a ground up sandstone from long ago which is rich in potassium...)) (Thank you Wikipedia.) Anyhow, I suspect a little extra nutrition will go a long way for you. Hopefully I will be able to report on the progress of my radishes shortly. I added bone-meal this spring, and so far my garden hasn't been dug up, hopefully I mixed it in well and didn't leave any lumps...

Here is a link that might be useful: Information about plant nutrients.

I would suspect that fertilizing would be a big help here as well. Just a little interspaced between the square - i put mine pretty much along the grid-lines - and then watered in would do you wonders.

I currently have two beds that were growing very slowly compared to the third bed and it dawned on me recently that because they tend to washout faster due to subsoil differences - two of them on only on 6" of clay above bedrock while the third has 18" of clay before you hit bedrock - as well as the fact that the compost for the two in question was from last years batch that they were a little nutrient starved.

In my case I put a little 2x strength fish emulsion along the gridlines of each and watered it in and in previous three days time I've seen almost double growth from the previous week.

Now I have a new problem, aphids are attacking my peas... :sigh:

Wood ashes at the base of your peas are supposed to help control aphids.
I really like the tire method for potatoes. Am trying it for the first time this year and plants look great, already four tires high on two of my four stacks.
There was another thread here or maybe in the vegie forum about radishes not bulbing up. The consensus seemed to be that the soil was too loose, provided no resistance, so the root just kept growing down long and skinny. My own experience seems to support this. I have radishes growing in three places, my conventional garden, lots of hard clay there, my sfg, and a container. The sfg and container are full of beautiful leafy plants, with little or no bulbs. The hard-pack clay radishes are amazing. Big bulbs that sit on top of the soil, with the long white root snaking into the ground. I have to pick almost every day to keep them from getting too large. So you might try something to 'thicken up' the soil where your radishes are. I'd post a link to the thread about this, but I'm a little PC challenged and don't know how. Sorry :)