When I do this, I keep both kites flat on the ground, bridle side up, LE into the wind. In this position, the kites stay put on the ground and there's no fighting the wind.
In more detail, I land inverted and stake the handles. At the kite, I'll stand downwind/behind the kite, bend over with my hands on the bridle side of the kite, pick the kite up by the leading edge, and push the LE into the wind. Now I've got the kite parallel to the ground, bridle side up, LE facing the wind. I'll set the kite down on the ground a couple feet into the wind from where it was, so there's a little slack in the lines. The kite I want to switch to gets placed in the same orientation, just downwind of the kite that's still attached to the lines. Usually I'll put it so the LE of the second kite is just underneath the bottom wingtips of the first. Now swap the lines over one at a time. If a line won't reach, move both kites upwind a little so the line does reach. Once done, slide out the first kite from under the lines and stand the second one up, inverted, ready to fly. The only part to be careful of is when sliding the first kite out not to snag a line. Hope that helps.
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