If I understand you correctly what you are doing is basically a lap joint, not a dado.
A dado is by def a crossgrain groove, such as one would make for a shelf or divider.
If you were making a true dado it would look like the pic with the sliding DT except it would be square. The problem with a lap joint centers around crossgrain gluing, which can result in the apron splitting if there is any wood movement (of course, with a 3" apron this is unlikely, but with a wider apron it is a real possiblity).
In furniture making, the basic idea is the joint itself is the structural part of the furniture, not a way to join two boards. We avoid the use of fasteners such as screws and nails and we don't fill holes.
There is a reason the M/T joint has been around for like 4000 years, and if you will give it a try, you will find it to be extremely strong and stable. If pinned or drawbored the M/T is just about the strongest joint on the planet.
If you don't want to go that route, then I would suggest dowelling as the next best alternative. One of the very first projects I ever made was a coffee table it was all dowelled together and 28 years later still rock solid. I remember when my boys were little them jumping up and down on it.