A couple thoughts:
The rabbet does not offer any support for lifting the assembly other than the short section of glue, which is an end grain joint. Even if you cut the slots and glue all the way across, there will be little support to lift with.
I would be afraid that the cedar would crack where you are cutting the grooves. Cedar is soft and crack prone to start with.
If you are not adverse to metal fasteners, brass screws would provide support, the heads would resist the joint pulling apart outwards, and the holes in all but the main anchor screws could be elongated slightly. The softness of the brass and wood combined will probably allow enough movement that the elongation does not have to be extreme.
Another option would be to use figure eight fasteners on the underside. However, the shortness of the screws in the underside of the large glue-up portion may not anchor well enough to resist pulling out. Might be hard to find figure eight fasteners that won't rust.
Third option would be to do a half rabbet (a dado half the thickness of the main panel), or extend the end pieces down below the main panel so the bottom shoulder of the dado would help support the main panel. This would still require some additional screws in elongated holes to keep the joint tight. The advantage of extending the side vertical pieces below the main panel is that it would better prevent the whole thing from rocking if the sink top isn't flat. Its a lot easier to plane off a little of the ends to get things to sit solid, than deal with a whole flat surface.
Fourth option if you are okay with the ends being proud of the bottom, would be to go with your initial design, but add a cleat front-to-back on the ends. The cleat would be about the same thickness as the side pieces, but twice the width, providing a ledge for the main panel to sit on. Screw/glue the entire length to the bottom of the side pieces, but just screws (with some elongated holes) into the bottom of the main panel to keep it in place.
With all the above, any glue on the main panel would be limited to about a 3" length, most likely at the back end to prevent the expansion from applying pressure to the vertical joint between the ends and the back.
Due to the fragile nature of cedar, you may want to consider making the end vertical pieces of a stronger/tougher material such as white oak to add strength to the shoulders of the dadoes if you go that route. However, this may add a lot of weight.
Now that you have posted a picture, I am sure others will come forth with better advice.
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