Agreed your soil may be on the alkaline side. A lot of wood ash, possible alkaline compost,and lime. Your base soil is glacial till probably with a lot of sandstone, schist, and shale and carboniferous rocks. It probably has a high water table so when it is wet it stays wet for a long time.
I am guessing based on your description and location that your soil is similar to this. Soil mapping has been done throughout the US and it helps to know the properties of your base soil. https://nesoil.com/images/pittstown.htm
I am very familiar with the big tops and no root phenomenon. I get it all the time.
If you grow nice fat leafy vegetables and your corn is tall then you have a lot of nitrogen.
Most root crops like beets like a sandy loam rich loam that is soft and the roots can easily penetrate. I think your amendments have created such a loam. Most crops like a pH between 6.0 and 6.8. Cabbages can stand it higher and beets do fine even if the pH goes up to 7.5.
Heres the thing about root crops, timing of nutrients is very important. If you want good root growth, you have to make sure you don't have a lot of excess nitrogen in the soil. You told us your amendments, but none of that would generate excess nitrogen. You must be adding fertilizer and the type of fertilizer matters for certain crops. Compost would actually suck up nitrogen as it decomposes.
I suggest this. Before you plant your next root crop, plant a scavenger crop like rapeseed, clover or radish as a cover crop to scavenge any excess nitrogen. Crimson clover or mustard should be planted thickly and tilled in when they start to flower. This will trap excess nitrogen in the crop residues and it will be released slowly back to the soil later.
Plant your beets and carrots. Beets 4 inches apart and carrots 2 inches apart. Do not fertilize until plants are 2 inches tall. We used sustane and bone meal. 4 parts sustane and 3 parts bone meal, but vegetable or plant tone by epsoma should work. You want something that is low nitrogen and high phosphorus. You only need about a teaspoon per plant. We made a thin line of fertilizer along the row. When the tops mature at about 5-6 weeks of age, the plant should be ready to start bulbing up, we gave it another shot of fertilizer. You can use epsoma garden tone or bulb tone instead. Bulbing plants need nitrogen to get good leaf growth in the beginning but to encourage bulbing there can't be a lot of excess nitrogen. So, the soil should be scavenged first of all excess nutrients that are left over from previous crops. When the plants are ready to bulb up is the next time they need a boost of fertilizer and some nitrogen, but not too much. Nitrogen will help with the phosphorus uptake if they are band fertilized. Getting the ratio right takes trial and error since a lot of that will depend on what is already in your soil. As a cheat I would use the garden tone for the first feeding and bulb tone for the second since bulb tone would have a higher phosphorus the second time around.
https://www.growing-life.com/shop/pH_and ... chart.html
If you get black rings in the beet flesh, it is a boron deficiency usually from a soil that has a high pH. Lowering the pH and adding micros will help.
https://www.ipni.net/publication/betterc ... %20p11.pdf
A soil test would be better since knowing your levels of phos, potassium and pH are important in terms of what fertilizer you use. If mother nature created your grow beds it would automatically be balanced. When humans start mucking around, thats when it gets messed up. A soil test takes the guesswork out so you will know exactly what you need to do to balance the soil again.
If I were to grow beets, I would need to use a scavenger but I would only add small amounts of nitrogen at the proper growth stages and no phosphorus at all since I already know my levels are way to high to add any more. My beets and root crops grow better in the alkaline plot pH 7.4 than the acidic one pH 6.0 mainly because the alkaline plots make nitrogen a little less available. On the other hand, the tomatoes are much happier in the acidic and nutrient rich plot. Leaf crops do equally well.
Happy gardening in Hawaii. Gardens are where people grow.