WI: WW2 Balkans strategy?

It's commonly known that in WW2, Winston Churchill espoused a strategy which included landing in the Balkans, presumably for geopolitical reasons (i.e. pre-empting potential Soviet influence in that sector.) This varied from his support for Greece in 1941 to espousing military landings in the Balkans (and things like the Dodecanese Campaign.)

The common wisdom on AH.com (which I also subscribed to until fairly recently) was that such an approach was extremely foolhardy. The terrain of the Balkans is rather awful for any sort of advance, and the front widens further and further as one advances, requiring the commitment of additional troops and potential overstretch.

However, there is one significant strategic point in favor of a Balkans landing that isn't usually considered: Chromite. Apparently, this strategic ore was crucial for the armament industry, and the German supply came entirely from the Balkans (Albania to some small degree, and primarily Turkey.)

To quote a U.S. State Department memo,

Although the Allies were unaware of it, President Roosevelt’s analysis of the importance of chrome to the German war effort was not nearly as devastating as that of German Minister for Armaments and Munitions Albert Speer, who reported on the current German inventory of alloy metals in a memorandum to Hitler on November 10, 1943, and concluded:

"Hence the element in shortest supply is chromium. This is especially grave since chromium is indispensable to a highly developed armaments industry. Should supplies from Turkey be cut off, the stockpile of chromium is sufficient only for 5.6 months. The manufacture of planes, tanks, motor vehicles, tank shells, U-boats, and almost the entire gamut of artillery
would have to cease from one to three months after this deadline, since by then the reserves in the distributions channels would be used up."

In his memoirs, Speer explained further that the conclusion in his memorandum "meant no more or less than that the war would be over approximately ten months after the loss of the Balkans."

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If Speer's analysis can be trusted, Winston's dream of a Balkans landing becomes much more realistic if the goal is merely to advance up to Albania and pressure Turkey into cutting chromite shipments to Germany (or block the shipments if Turkey is unpersuadable), and then simply wait until Germany collapses.

Thoughts? Was a Balkans landing actually a viable war strategy?

One thing wants to tell me the logistics and terrain would make it a worse Italian campaign, but the partisan fighting in the Balkans makes things interesting.

A Balkan invasion campaign would have been a major undertaking if the interdiction of chromite ore shipment is the reason. Diplomacy, bribery, spies and bridge-busting bombers could achieve the same goal at a fraction of the cost in blood and gold.

Just Leo said:

A Balkan invasion campaign would have been a major undertaking if the interdiction of chromite ore shipment is the reason. Diplomacy, bribery, spies and bridge-busting bombers could achieve the same goal at a fraction of the cost in blood and gold.

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The thing is, Allied sabotage and strategic bombing campaign attempts weren't exactly the most accurate or effective in WW2. Then again, they didn't quite know that at the time either.

Perhaps the question should be, "What would happen if the Wallies seriously pursue a Balkans strategy, and the potential collapse of Germany thanks to chromite deficiency was an unexpected bonus?"