First of all, congratulations on killing a shooter and that is a beautiful picture and food plot!
I'm not sure I follow the question about the rape and chicory though. Did you want to include both with the ladino replanting or just chicory?
Rape is better suited as a late summer planting where it can grow and mature as the weather cools. It doesn't like the heat of late spring/summer and with the long days, it will rapidly mature and become useless to the deer. Plus, I consider rape or any brassica as unwanted competition with newly planted clover.
Chicory and clover planted together makes a great combo though. During the heat of summer and especially dry spells when the clover struggle's, the chicory will still be producing and attracting deer. But as you mentioned, over time the clover will crowd out the chicory. Since your clover stand has some age on it, frost seeding chicory now or in the next few weeks might be an option.
Earlier, you had mentioned a new plot going in a old pasture. If that is still the plan, then I would definitely keep this plot going for at least another year.