I have a lawn, about 40 yards x 20 yards. It is on a 2-way slope (top to bottom
and side to side) which varies in its angles. The underlying soil is clay. It
is now both compacted and rather wet, and the grass is looking tired and is
yellowing. It contains a variety of grasses, including couch, and some moss. It
is also rather undulating I want to improve it (a) to get a better lawn
(presumably by improving the underlying soil) and (b) to get a constant slope,
with the undulations. Questions:

1a. Can I just rotovate it, add grit-composted bark-other elements and sow new
seed?
1b. If so, at what time of the year should I do that?

OR

2. Should I kill the whole thing with, say, Glyphosate, and then rotovate etc.
Again, when should we do that? This second option involves more work, but if
that would make a substantial difference, I'll do it.

Any suggestions, comments, or ideas?

With thanks

Laurie