Where should the legs go on an L-shaped desk that has to be taken apart and moved often?

On span: solid hardwood at typical desk thickness is quite stiff, and the spans in your dimensions are still substantial. Two things help without adding legs:

An apron or rail under the front and back edges of each top. A rail on edge is enormously stiffer than the same wood laid flat, and it is what stops a desk top from deflecting under a leaning elbow. On a knock-down design the rails can be bolted rather than glued.

Keep the overhang modest past the outermost legs. A long unsupported overhang at the end of an arm is where deflection is most noticeable, because it is the point furthest from any support.

For solid wood specifically, also allow for seasonal movement across the width. Fix the tops to the frame with fittings that permit the panel to expand and contract — slotted holes, buttons, or figure-eight fasteners. Bolting a wide solid panel rigidly at both edges is how tops crack, and a desk that gets moved between climates is exactly the case where it happens.

The corner is the whole problem, and it is worth being explicit about why.

An L-shaped desk is two panels meeting at right angles. Each panel is stiff in bending along its length and neither resists twisting at the joint on its own. When you lean on the far end of one arm, the load path runs through the corner, and if the corner is not supported and not stiffly joined, the assembly racks — the two tops move relative to each other and the whole thing feels wobbly regardless of how solid the panels are.

So: put a leg at or very near the corner. That is the single most important placement decision, and skipping it for legroom is the most common mistake in these builds.

After that, a leg near each free end, giving you three or four support points. The unsupported spans between them then determine whether the tops sag.

For the repeated assembly requirement, the hardware choice matters more than the joinery.

Threaded inserts in the tops, with machine bolts through the frame, are the right answer. They can be undone and redone many times without wearing, unlike wood screws, which lose grip after a handful of cycles in the same hole — and that loosening is exactly what makes a knock-down piece feel worse each move.

Make the corner joint a bolted connection with locating dowels or a shallow rebate, so the alignment is mechanical and the bolts only clamp. Relying on bolts alone to hold alignment means it goes together slightly differently every time.

Number and mark everything on hidden faces. After the second move you will not remember which leg goes where, and getting it wrong once and forcing it is how holes get enlarged.

One thing about the tops themselves, since you are gluing boards up: pay attention to how you arrange them before glue-up.

Alternating the growth ring direction between adjacent boards is commonly recommended to limit overall cupping across a wide panel. Matching colour and grain across the joints matters for appearance, and on a desk you look at it for hours.

And finish both faces equally, including the underside. A panel sealed on one side only takes on moisture unevenly and will cup — which on a desk that moves between houses and climates is a real risk rather than a theoretical one.