When I was 300 lbs I paddled kayaks rated at 300 lbs but when I moved up to a slightly longer kayak at a 350 lbs rating the experience was a lot more enjoyable, even just for mellow lake trips. You probably won't sink it at the limit -- it may make the ride wet and a bit slower. If you just want to paddle mellow lakes then you should be fine. You do want to test if you can get back in the kayak when you are in deeper water. I have friends who are consider themselves active and fit but are probably really just average, that really struggled getting back on SUPs and SOTs in deep water.
You might want to check out the Perception Tribe 13.5 Tandem. It has a 500 lbs weight limit and is $650. I frequently see it for $550 on sale. It has 2 seats and spots for 3. Just move the seat to the middle for a solo paddle. Seems like REI and EMS carry this kayak.
The Perception Sport Rambler 13.5 looks like a cheaper version of the Tribe, might even be an older version of the Tribe but i didn't think the Tribe was that old. It sells for $450 and supposed to be at Dick's but ours up here never have them.
I have never tried either kayak but seems to be in your specs.
The Perception Sport Pescador seems to be an older version of the Tarpon. The Tarpon always seems to be a popular and well regarded SOT.
Kayak Kaboose Trailer
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