If it turns out to indeed be a port tack reach out and stbd tack reach back with marks to port, you've really no choice but to hoist a jib, douse the kite, tack around and reset.
In actuality you'll probably find at least one of these legs too tight to make the kite worthwhile. Keep an eye on the angle of the halyard to the centerline of the boat. if the halyard lead has any aft component, you're probably better off with a headsail. As long as it angles forward from the masthead and control isn't an issue it may be paying off.
Try it! You'll like it!
1984 Fast/Nicholson 345 "FastForward"
".. there is much you could do at sea with common sense.. and very little you could do without it.."
Capt G E Ericson (from "The Cruel Sea" by Nicholas Monsarrat)