"though nonetheless" is correct and usable in written English.
You can use it to introduce a contrasting idea after you have made a statement. For example: "I'm not usually a fan of amusement parks, though nonetheless I had a great time at the fair."
Bonuses, though, nonetheless.
Everyday wines tend to be simpler, though nonetheless satisfying.
This influence was reinforced by an indirect, though nonetheless profound, Islamic propaganda.
That appears to be the only difference between the two wines, yet this one was altogether simpler, though nonetheless pleasant.
It has predictable though nonetheless extraordinary parallels with the Abramovich-Berezovsky case, which is still playing out in a courtroom on the floor above at the Rolls Building.
Last month, when Paul Ryan's lament over the laziness of "inner-city men" sparked a smaller controversy, he followed his remarks with a barely credible, though nonetheless effective, disclaimer that he wasn't referring to any particular racial group.
There will be eclipses nonetheless, though not as glorious as the one approaching; we should be so lucky as to last long enough see them.
(In Australia's case the impact on saving is not clear cut: the saving rate has fallen nonetheless, though arguably by less than it would have done without the mandatory component).
It's nothing ground breaking, but a cool feature nonetheless, though, you can sweep through menus by sliding your finger up or down.
Other evidence, though meagre, nonetheless suggests several processes that contributed to the increasing cohesion.
"I don't enjoy looking back," he said, though he nonetheless seemed compelled to do so.
