If you do square foot gardening it is designed for maximum yield in minimum space does require you to tri whatever falls outside of the space. As you have learned already the other downside to close spacing is that air circulation can be a problem unless you choose your plants well and it actually helps not to plant all the squares at the same time. It will give the larger plants more space and younger plants between older plants don't' take up that much space...yet.
The other thing with close spacing and not having an established garden patrol yet is you have to constantly be on the lookout for pests and disease and nip it in the bud.
I actually give my zucchini plants a 3 foot circle. In my garden that is one of the quarter sections and they are planted so half the zucchini is going to be sticking out into the path. It is fine if I am not using all of the garden space, but I prefer to put large plants like zucchini, and tomatoes outside the garden in their own space instead.
I don't like to thin, but if I plant carrots I either have to thin or really spread the seeds when I plant them. Carrots will need about 2 inches of space between them otherwise you may not get a lot of carrots because of crowding.
Carrots are hard to transplant, so it is worthwhile to get pelleted seeds. For myself carrots have such a short planting window, are relatively hardd for me to grow, they don't taste any better, in fact mine can be bitter, and they are inexpensive to buy so I don't plant a lot.
Beets, lettuce, Asian greens and some herbs are fairly easy to transplant out and since I am succession planting in the garden. I start the seeds in community pots and transplant out into the garden when the previous crop is done. The square foot method allows you to amend and plant just one square at a time. Planting seedling starters increases yield because you save time waiting for the seeds to grow and while the garden is occupied with the previous crop, you can get a head start on the next square. The hardest thing in doing that it helps if you keep good records of what you have planted where and especially when they germinated. That way you can estimate days to harvest when the square will be available. It is something I still have to work on. Sometimes things took longer to fruit than expected especially when the weather was colder than normal so I ended up having over grown starts. I partially solved that problem by giving some of them away and I have learned to plant a couple of starts a couple of weeks apart and to wait a little longer to start them. I sometimes start more than I can plant out in the allotted space, so now I try to leave a section open a little longer for the overflow and I will plant seedling between other plants wherever there is space.
It takes a while to figure out how much space each plant actually needs. Square foot gardening helps with that but you have to plant evenly in the square so things are not bunched up. The exception in my garden is that the tomato trellis I use for the cucumbers can support more than one cucumber so I plant 2-4 on the same trellis. I don't use commercial tomato trellises for tomatoes, but they are good for pea fences when they are opened up or for cucumbers, pole beans and to support bell peppers. I don't use the cone tomato trellis, only the folding tomato trellises, they are easier to store, can be used in different configurations for other plants, and are stackable (sort of) .
I find that the square foot spacing is a little too tight and I don't like to plant in rows, thin or prune. I give plants a little more space. Things like cucumbers, don't need the whole square if they are trellised up. So if the trellis is on the north side, they only need to be planted along the edge of the squares. you can plant something else in the same square around the cucumber. The square foot plans are not designed to plant more than one thing in a space.
Large plants like zucchini, squash, melons take up too much room in the garden so they have to have their own space somewhere else, I plant tomatoes in large pots instead on in CRW cages (no pruning required). Melons I let sprawl and at my community garden I have an overhead trellis they can climb on and I can still plant under the trellis. The gourds will climb the perimeter fence. Of course I lose a few of the squash that way too. I have an open space near the garden gate. I can plant melon or squash vines on the edge of the garden and they can sprawl in that space. I can't plant too near the fence or my plants would end up being harvested for me and that section of the garden was where the tool shed was and there are rocks and buried concrete tile and iron in the ground so it is not that plantable. After a while you will find you grow more or less the same kinds of things and you will know how big they get and how much space they need at maturity and it becomes easier to space things that way. Bush beans for one I would only plant one in a square so they move more air between them. Mostly I grow pole beans since they produce more beans and they take up less space on a trellis. Cowpeas will sprawl out about three feet but they can climb on each other so I give them a 3 ft wide strip. It is easier for me to work the garden if I don't have perennials mixed with annuals so I keep herbs and long term crops like jicama, ginger, taro, tomato, peppers, citrus trees in pots. It is easier to work around in the garden if you don't have to work around long term plants. Ginger and heirloom tomatoes cannot tolerate nematodes and taro and sweet potatoes would be all over the place so they are better contained. Citrus trees in pots keeps them smaller and so I can have more varieties but the yield drops with the size.
Over time instead of squares, I look at my space in terms of circles. Plants really don't grow square without pruning.
I have a 3 foot diameter circle for zucchini, cutting celery, kale, broccoli, brussels sprouts. If I plant on the edge of the garden the circles can go out of the box.
I have a 10 inch circle for lettuce, tatsoi, spinach
I have a 2 ft circle for mustard greens, daikon, swiss chard
2 inch circles for carrots
4 inch circles for beets, radishes
Since I trellis cucumbers, beans, peas, jicama, 2-4 plants can be planted in a 1 ft circle. If I use the tomato pots for these instead I can get about 9 plants on a tomato trellis.
I can plant smaller circles inside the large circles when the bigger plants are still young.
Happy gardening in Hawaii. Gardens are where people grow.