Take a look at Tom Yost's site: www.yostwerks.com. you could probably fit any of his 15' to 17' boats. He like his boats to have low decks for easy rolling. That also makes them low volume. Since his "plans" are in the form of coordinate points which you will need to graph out before you build anything, you can pretty easily draw what he has, then tack an inch or inch-and-a-half to the height of the sides (just extend the lines) and raise the center of the deck by about the same amount.

That gives you a boat which is just as wide at the water line as his design, but which has a bit more ability to recover stability, or it will be a bit more difficult to roll. It will also have a greater carrying capacity as it will be sitting about 3/4" to 1" deeper than its design waterline. Probably around 4" to 4.75" when you are paddling. With your weight and the weight of the boat you'll probably displace 300 to 315 pounds.
Load up with camping gear and you'll be in around 350 to 380. Just a "ballpark estimate', but most kayaks sink an extra inch for every 85 to 95 pounds added to them. If the design waterline is at 3 inches, you can usually add 200 pounds over the "design" displacement and have a stable craft. But, that will sink you about 2" deeper than the design displacement. As long as the sides are high enough there should be no problems.

If you look at the "expedition" versions of some of Yost's designs you'll see that he has already done the alterations for carrying more weight. (higher deck, etc.)

If your situation leaves you with fewer days, but about $250 more in the budget. You should consider building an aluminum-framed version of whatever Yost design you pick. You'll spend about $300 for aluminum tubes from Texas Towers, as opposed to about $50 for lumber for the frame. You can make the frames from solid HDPE (High Density PolyEthylene) as Yost shows, and spend about $100 on the plastic, or you can make the frames from plywood, and cut up pieces of HDPE cutting boards (Under $5 at Walmart) for the attachment points. (screw or bolt them to the plywood).

The aluminum frame can be left together at all times, or taken apart for storage or travel. It takes about 30 minutes to assemble each time. Less once you are used to it. That makes it a wonderful 3rd boat. Put two boats on the roof racks and throw the third in the trunk. While the rest of the family is unloading the roof racks you'll be 10 minutes into assembling the folding boat.

The aluminum needs to be cut to length. and have a few rivets installed. No sanding, no varnishing. Dropping those operations really speeds up the building time.

Just a thought.

PGJ