Logic Masters Deutschland e.V.

This puzzle was created as part of Scojo's imposter prompt, where me and someone else had to create a puzzle in my style, and then people would guess which is mine. The opposing puzzle was created by Agent, and can be found here.

Rules:

• Doc takes his DeLorean for a time-travelling trip around the A38.
  The DeLorean starts at the black circle, then travels around the grid, passing through every cell without a number, before ending back at the circle at the same point in time.
• The DeLorean travels orthogonally and moves at a rate of one cell per minute.
  Whenever it enters a grey cell it travels back in time 10 minutes.
• In order to enter a grey cell, it is required to have a time travel permit. Permits are obtained from cells orthogonally or diagonally adjacent to number clues.
• A number clue N indicates that Doc acquires a Permit in the Nth neighbouring cell that the car passes through. (From a chronological perspective, not the perspective of the DeLorean).
  If there is a tie for the Nth cell passed through, a permit is only picked up in one of them. (This may result in the positions of some permits being unresolved, despite the path being unique).
  Permits cannot be obtained in a grey cell.
• A clued cell must have a clue for each permit adjacent to it, and each permit must be clued by at least one number clue.
  Doc cannot hold more than one time travel permit at a time, and going back in time uses up the permit.
  Note: the time travel occurs and permits are used up when entering a grey cell, i.e. when crossing the cell border.
  At the start and end of time, Doc holds no permit.
• Note: Permits are stored online at the time of purchase and thus don't need to be physically brought to where the time travel occurs.

For additional clarification, an example of a completed grid is given.
Red numbers show the time at which the DeLorean is at each cell, green numbers show the order the cells around each clued cell are reached (for 3 of the clued cells, to avoid confusion from the overlap). The coloured (non-grey) cells match the permits with the cells immediately before they are used.

Main puzzle:
Penpa link: Click Here