A mower is nice to have, and a good practice to manage clover.. but it is not a necessity.
Are you wanting to rotate this fall yet, or will you have brassicas still, this fall?
If the "first", I'd go ahead and broadcast clover seed this fall.
Clover seed is tiny, and does just fine broadcasted. Add some winter rye, if you are wanting this as a plot to hunt over.
Look to the Heavens, As there lies the true answers in life. No mountain too tall, no ocean too wide.
And I, obsessed with the land, but dedicated to the One who created it.