Another problem is the amphibious forces, Britain had LST Mk3 and LCT Mk 8, both slow and small types with no LPDs as they were Lend Lease and returned to the US after WW2. A couple of LPDs, given to the British under MAP would have been very valuable during Suez, especially for a quick reaction operation.
It is true that Britain's amphibious force at the time of Suez was built around the LST(3) and LCT(8) with max speeds of 12-13 knots. But there were also 11 merchant cargo liners engaged as troopships (the equivalent of many of the wartime LSI(L))
Beyond that I think you are getting a bit muddled. There are two types of ship. The LSD and the LPD.
It was 4 x 16-17 knot LSD that were supplied to Britain in WW2. These were great for carrying smaller craft (e.g. 3 x US built LCT(5) or 14 x LCM(3), DUKW etc) but their troop accommodation was very limited (about 240). The USN laid down another 22 for their own use in WW2.
The successor to the wartime LSD, the Thomaston class laid down from 1954 was faster (22 knots) but still only had accommodation for 320 troops. The USA didn't begin to lay down the first of the 20 knot Raleigh class LPD until 1960. It was them that had troop accommodation for 1,000 men.
In the 1950s the USN amphibious fleet was still very much built around wartime construction. LSD (see above), LST(2) (10-11.5 knots) plus a couple of dozen slightly larger & faster versions buiit around the mid-1950s, LSM (13 knot), the 16 knot AGC, the APD High Speed Transports (24 knots) based on the DE hull with accommodation for about 162 troops, and the Haskell class APA (17-19 knots, troop capacity about 1,560). It took the presence of all these types for the USN to mount a successful amphibious operation.
The WW2 RN equivalent of the APA was the LSI(L). Being converted from requisitioned merchantmen, they had all been returned to their owners in the immediate post war period. The RN equivalent of the AGC at Suez was the LSH(S) Meon, a converted River class frigate (the RN also had a pair of LST(3) converted for the role).
So, even if the RN still had a couple of LSD, I'm really not sure how you see a force of less than 500 men having much of an influence on things at Suez given what is really a marginal difference in speed over the 1,000 miles or so from Malta.