Oh I see what you mean now, indeed:

    Score: 7
    ~~~~~~
    ~····~
    ~·~~·~
    .#..#.
    ......
    ..#...
    .#H#..
    ..#...

However, I think that you do not need 'time' based variables in the form of

    reachable(x,y,t) = reachable(nx,ny,t-1)

Enforcing connectivity through single-commodity flows is IMO better to enforce flood fill (also introduces additional variables but is typically easier to solve with CP heuristics):

    Score: 2
    ~~~~~~
    ~....~
    ~.~~.~
    ......
    ......
    ..##..
    .#H·#.
    ..##..

Cool puzzle!