w/out Suez, how long does Eden last?

This depends on exactly how the Suez Crisis is avoided. Does Nasser back down? Highly unlikely in my view.
The POD has to be earlier, during the Churchill premiership probably, and would entail an acceptance that the British Empire was no longer viable (in reality it hadn't been viable since the Great War). Churchill would never do so; he was an imperialist. Therefore the best POD would seem to be an earlier Churchill retirement, probably by pressure from his wife.
How much earlier? At the very least, two years in order for Eden to set in place his own policies.
Eden would, I think, have been a satisfactory Prime Minister; his fate was tragic.
 
Theoretically, a compromise solution for the Suez crisis was possible on the basis of the "Six Principles" passed by the UN Security Council on October 13, 1956:

Any settlement of the Suez question should meet the following requirements:

1 there should be free and open transit through the Canal without discrimination, overt or covert — this covers both political and technical aspects;

2 the sovereignty of Egypt should be respected;

3 the operation of the Canal should be insulated from the politics of any country;

4 the manner of fixing tolls and charges should be decided by agreement between Egypt and the users;

5 a fair proportion of the dues should be allotted to development;

6 in case of disputes, unresolved affairs between the Suez Canal Company and the Egyptian Government should be settled by arbitration with suitable tems of reference and suitable provisions for the payment of sums found to be due.
Source: Lloyd, 1978, appendix IV, p. 276

"Given what was to follow, it is ironic that these principles were to form the basis of the ultimate settlement of the Suez Canal dispute in 1957. The proposals, on the surface, represented a satisfactory reconciliation of the *public* British position and that of Egypt. What they did and could not do, however, was administer a public humiliation to Nasser that would lead to his downfall which was the *sine quo non* of the *private* British position. Although these principles were greeted by Eisenhower with an enthusiastic endorsement that this meant that the crisis was over, no agreement was reached on the system that would administer the Six Principles. None the less, this represented a considerable advance on the diplomatic deadlock of the preceding months and Eden consented to Lloyd remaining in New York to explore further avenues of progress with Fawzi, the ultimate aim being that if sufficient progress had been made the foreign ministers should meet again at the end of the month. This was potentially embarrassing as Eden had delivered, on the very same day as the passage of the six Principles by the Security Council, a speech to the Tory Party conference at Llandudno which, in refusing to rule out the use of force, was, as Carlton notes, greeted with such great enthusiasm by the delegates that the Prime Minister must have realised that any compromise solution, such as Lloyd was working towards in New York, would be deeply unpopular in the Conservative Party..." https://books.google.com/books?id=d7xyYQ6XhsAC&pg=PT102
 
Theoretically, a compromise solution for the Suez crisis was possible on the basis of the "Six Principles" passed by the UN Security Council on October 13, 1956:

Any settlement of the Suez question should meet the following requirements:

1 there should be free and open transit through the Canal without discrimination, overt or covert — this covers both political and technical aspects;

2 the sovereignty of Egypt should be respected;

3 the operation of the Canal should be insulated from the politics of any country;

4 the manner of fixing tolls and charges should be decided by agreement between Egypt and the users;

5 a fair proportion of the dues should be allotted to development;

6 in case of disputes, unresolved affairs between the Suez Canal Company and the Egyptian Government should be settled by arbitration with suitable tems of reference and suitable provisions for the payment of sums found to be due.
Source: Lloyd, 1978, appendix IV, p. 276

"Given what was to follow, it is ironic that these principles were to form the basis of the ultimate settlement of the Suez Canal dispute in 1957. The proposals, on the surface, represented a satisfactory reconciliation of the *public* British position and that of Egypt. What they did and could not do, however, was administer a public humiliation to Nasser that would lead to his downfall which was the *sine quo non* of the *private* British position. Although these principles were greeted by Eisenhower with an enthusiastic endorsement that this meant that the crisis was over, no agreement was reached on the system that would administer the Six Principles. None the less, this represented a considerable advance on the diplomatic deadlock of the preceding months and Eden consented to Lloyd remaining in New York to explore further avenues of progress with Fawzi, the ultimate aim being that if sufficient progress had been made the foreign ministers should meet again at the end of the month. This was potentially embarrassing as Eden had delivered, on the very same day as the passage of the six Principles by the Security Council, a speech to the Tory Party conference at Llandudno which, in refusing to rule out the use of force, was, as Carlton notes, greeted with such great enthusiasm by the delegates that the Prime Minister must have realised that any compromise solution, such as Lloyd was working towards in New York, would be deeply unpopular in the Conservative Party..." https://books.google.com/books?id=d7xyYQ6XhsAC&pg=PT102
According to D R Thorpe's biography, Eden did not believe Nasser would keep to the Six Principles; further as most of Europe's oil supply passed through the Canal he probably considered he was acting in Europe's, not just Britain's interests. Of course, the United States had different interests; very little of its oil supply was affected.
The timimg of the Suez action was unfortunate, to say the least. The US Presidential elections were in progress and Uncle Ike was running on a "safe pair of hands" platform; although Dulles had indicated previously that the US would not stand aside...interpreted by Eden as support.
As for Eden's health, he had had an operation where his bile duct had been severed in 1953; it was not properly repaired until after Suez. It caused him trouble.
As for his domestic policies, he espoused a "property owning democracy" and policies of full employment. He had, after all, grown up in the North East of England and knew of the dire living standards of the working class. My view is he would have been progressive, but cautious with the economy.
 
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