Attaching 3/4" engineered flooring to a 2" Doug Fir stair tread at the top of a landing can be challenging, but your idea of routing a groove into the tread and gluing a spline in place could be a viable solution.
Using a spline can help distribute the weight and pressure of foot traffic more evenly across the stair tread and the engineered flooring. This can help to reduce the likelihood of the flooring separating from the tread over time.
When routing the groove, it's important to make sure that it is the correct width and depth to fit the spline securely. The depth of the groove should be slightly shallower than the thickness of the spline to allow for expansion and contraction of the wood.
To ensure a strong bond, you will want to use a high-quality adhesive specifically designed for wood flooring installation. Apply the adhesive to both the spline and the groove, and then insert the spline and press it firmly into place.
drywall finishing fort worth txOnce the spline is in place, you can glue the first piece of engineered flooring directly to the spline. Be sure to follow the manufacturer's instructions for the adhesive and allow sufficient drying time before walking on the flooring.
Overall, using a spline to attach the engineered flooring to the stair tread can help to strengthen the connection and improve the longevity of the installation. However, I would recommend consulting with a professional flooring installer to ensure that this approach is suitable for your specific situation.