I see that you and Pat have been posting while I have been typing. With the new information, some of what I say will not be all that valid for you, but I'll post it anyway. You may pick something out of it that may help you.
You can easily overthink this kind of stuff. And don't forget here is a lot of personal preference in what I am going to say. Somebody else would lay it out totally differently than I would for different but perfectly valid reasons.
Don't beat yourself up about it. It is your first year. Even after ten years, you will still have some successes and some things that could have gone better. And don't worry about having just six beds. You can grow a lot in them without being overwhelmed your first year.
I think all of your beds are 4x8 but I am not sure how close together they are. Your sun will be coming from where you have the corn, that being on the southwest side. Are the beds close enough together that the corn will shade the bed just northeast of it? If you trellis, cage or stake your tomatoes or cucumbers, they might also offer some shade to another bed. It is probably nothing to worry about, just something to maybe consider when laying it out.
Cucumbers, watermelon, and pumpkins can come in bush or semi-bush varieties that run a lot less than others, but production is usually a lot less too. You'll be amazed at how much a regular watermelon or pumpkin will run, while the cucumbers will get thicker rather than run real long distances. The big problem for me is that you cannot really keep grass and weeds cut so where they go tend to get real messy. You can trellis the cucumbers and keep them better controlled, but they still tend to wander.
I kind of like the way you laid it out. The corn will finish long before the pumpkins and watermelon so they can run that way. Shade from the corn should not bother them, especially after they start to run. I don't know how much production you are after from the watermelon and pumpkins. For your first year, especially if you go with the regular ones instead of bush varieties, I'd be tempted to put half of one bed in pumpkins and the other half in watermelon.
I would be tempted to put the pumpkins and watermelons where you have the corn and the corn where you have the pumpkins. The corn will finish fairly early compared to pumpkins and watermelon. Having it there may give you better access to plant a fall garden, but I think Pat is right. The watermelon and pumpkins will probably be over there too. They just don't take discipline well, especially if you get the non-bush types.
Another alternative is to plant the pumpkins with the corn. The pumpkins will provide a sort of living mulch for the corn once they take off. One potential problem is that the pumpkins may make it a little hard to get to the corn for harvesting if they really take off, but I'd expect you to be able to manage that without any real inconvenience. I've never tried watermelon with corn. Somehow that just doesn't feel right, but I'm not sure why. Maybe the watermelon need more sun at a young age? But growing pumpkins with corn is an old practice, although that was traditionally field corn, not sweet corn. You might want to notice how much the pumpkins are spreading when you harvest the sweet corn and file that information away for next year. See what I mean about overthinking it?
There are so many different ways you can do this and practically any of them will work well. Don't overthink the shade thing. That probably will not be an issue. If it is, next year plant something there that needs a little less sun in that shade. The way the watermelon and pumpkins spread is about the only thing I think will surprise you about growing them.
This is your year to get a handle on how much of anything you want to plant. You may find that a very few pumpkin plants make all the pumpkins you need. Maybe not. If all you want from the beans is some to eat on, one full bed may be too many, but if you are into canning, you may want more. With the corn, if you are preserving it, you want to plant it all at one time, but if all you want is fresh corn to eat, you will probably do better planting half or even a third of the bed at one time so you get a staggered harvest. Maybe plant each planting two weeks apart.
Good luck with it. It is an adventure, but there is nothing like sweet corn going straight into the boiling water. I think you will enjoy the adventure, even with an occasional frustration along the way.
The "bush" part of their name does not mean each plant gets big and bushy, it is simply telling you they are very short as opposed to tall vining sprawling pole-beans or runner beans 
