I'm concerned about (1) the strength of the hatch cover, and (2) compromising the strength of the deck.

I wouldn't be too concerned about either of those strength issues.
If you are using the typical construction style - cutting out a piece of deck and then use that for the hatch cover- the 'ledges' that you add to the underside of the deck will add quite a bit of strength. If the hatch cover doesn't hold its shape , you can add a couple of little 'beams' to the underside to maintain the curvature.

How does this look to you guys?

I prefer the more oval or even round hatches; perhaps I'm biased because I use commercial hatches. Look at some of Rob Mack's or Nick Schade's hatches - it's not necessary to have the hatch follow the stripe pattern of the deck to get an attractive result. And, I think that hatches without 'corners' are probably stronger.
About hatch size :
I'd think about the maximum size objects that might go into the compartment - sleeping bag in stuff sack, bear barrel for food, kayak wheels and/or frame, tarp poles, hiking poles, etc.. Also, it's very nice to be able to work through the hatch when you are filleting the bulkheads or other interior work. You could check on some commercial hatches for size ideas.
About hatch placement:
Unless it's necessary because you are adding a 3rd compartment ('day hatch') just behind the cockpit, it's useful to keep a clear deck there for a foot or more, to facilitate rigging for paddle float rescues.
It's nice to be able to reach into the ends of the boat to grab gear, but in a longer boat you'll probably need to use some sort of stick and hook to retrieve items from the ends anyway.
Does you boat have a skeg? Might you add one later?
If you are using your boat for day paddling and don't have a 'day hatch' compartment, partially inflated float bags or a few dry bags filled with bubble wrap, pushed into the ends of the boat can keep your lunch, spare gear and water near the hatch opening, and closer to the center of the boat.
I've done a few short trips in an NDK Romany which has only round 9.5" hatch openings, and it does affect the ease of packing, so you'll need to adjust your dry bag choices to match the hatch openings on your boat.