Hi All,
Glad this topic might be coming back to life because I agree with David, the "workaround" is way too arbitrary to be considered a solution, and it doesn't work with control point splines or projected splines...
However, Chris, it looks like you posted a better solution back in June 2018.
Your solution was specially for a circle tangent to a spline, but you can easily use the same logic to make it works with line tangent to spline, see the picture attached below.

However, I'm having a very hard time making it work with control point splines...it either gets (falsy) over constrained or I can't move the construction around the spline...
Surprisingly tho, if I build the spline first, and then build/constrained that tangent on a second sketch, then there is no problem at all...very frustrating, since it's not always possible to split the sketched constructions...
One way or another, it would be really great to have it working with a simple constraint and any type of splines, especially since most CAD softwares can do it for years now...