My 10-step program:
Step 1. Agree on a unified Mediterranean strategy after the Fall of France, acknowledging that Sealion will never work. This should butterfly away the invasion of Greece if it includes a unified deployment into Romania
Step 2. German forces sent to Libya prior to Operation Compass, enough to prevent disaster.
Step 3. [after Rashid Ali's coup in Iraq] German paras deployed to Rhodes
Step 4. German paras take literally undefended Cyprus
Step 5. Using Cyprus airfields for air cover, transport limited forces to Syria and Iraq, even if solely by air and a few blockade runners
Step 6. Advance up to Mersa Matruh in Egypt, then stop
Step 7. Park the entire Stuka fleet at Mersa Matruh and start using it to bomb Alexandria
Step 8. Rinse and repeat until the Royal Navy abandons Alexandria, thus ceding naval supremacy in the eastern Med to Italy
Step 9. With the sea lanes now secure, start shipping troops and supplies to Beirut
Step 10. Take Egypt from the east
I suspect the 10 point program is a little tongue in cheek but fun to look at.
1) This helps Barbarossa too. (less aircraft losses, hundreds less, no BOB, no Crete)
2) At a minimum, a good battalion of 88 mm guns to deal with the Matilda tank would help a lot. The British attacking force in Compass is an infantry and an armored division, one good small German division to back up the Italians should be enough to hold the Libyan frontier.
4) Concerned about Rhodes airfield capacity. Greece is neutral though which helps supplying the island. Dropping a regiment a day on Cyprus from Rhodes is all I can see. The British would certainly throw forces in if they figured out what the Germans were up to. They would notice the activity about Rhodes, without a Greek distraction of their own might reinforce the island enough to contest this.
3+5) Probably best for Rashid Ali to just not provoke the British, remain neutral, still be a source of Axis Intel in the area (the Italian embassy was still open in Baghdad), No Iraq means no Syria (remain Vichy). No way the Germans could ever match British power deployed from Basra with just road supply from Beirut.
6+7+8+9+10) I imagine the British would move their big units south of the Suez canal while keeping their destroyers and submarines in Palestine to attack axis shipping. Basing enough air units close to Alexandria is the hard part.
You have to get all this done by May 41 to be able to do Barbarossa.
I like your #1, #2, but diverge after
Step 1. Agree on a unified Mediterranean strategy after the Fall of France, acknowledging that Sealion will never work. This should butterfly away the invasion of Greece if it includes a unified deployment into Romania
Step 2. German forces sent to Libya prior to Operation Compass, enough to prevent disaster. (1 Panzer division with supporting 88 batteries, about 50 ME109s, 50 Stukas)
Step 3: Use this division and the Italians to establish a blocking position on the Libyan, Egyptian frontier.
Step 4: Do Barbarossa two weeks earlier than OTL, with hundreds extra bombers and hundreds of extra JU52s not lost in Crete, and less trucks needed in Africa, and the extra divisions not returning late from the Balkans.
Step 5: With the extra forces in Step #4. Take Moscow in 1941
Step 6: Follow up operations in 1942 to cripple Soviet unions ability to counter attack.
Step 7: Defeat or at least contain in the Bocage the Normandy invasion in 1944
Step 8: Hope that since you are still in France and have poison gas you can stick in rockets, hope the Allies don't use the Abomb out of fear of retaliation.