It is possible to climb the left side of the room with SpeedBooster alone, with either a tricky dash jump or a vertical shinespark.

Requires:

"Morph",
{"or": [
  "SpaceJump",
  "canSpringBallJumpMidAir",
  "canWallJump",
  {"and": [
    "HiJump",
    "canSpeedyJump"
  ]},
  "canIBJ",
  "canTrickyDashJump",
  {"and": [
    {"canShineCharge": {
      "usedTiles": 28,
      "gentleUpTiles": 3,
      "gentleDownTiles": 3,
      "openEnd": 0
    }},
    {"or": [
      {"shinespark": {"frames": 18, "excessFrames": 8}},
      {"and": [
        "canSpeedyJump",
        {"shinespark": {"frames": 16, "excessFrames": 10}}
      ]}
    ]}
  ]}
]},
"h_heatedGModeOpenDifferentDoor"