Placing 1d items in a 2d grid with constraints
The 1-dimensional case (a $1 \times n$ grid) is straightforward.  I'm not sure why you are having difficulty finding solutions when the grid is 1-dimensional.  If you don't have any constraints, then you just add up the lengths of the items; if their total length is $\le n$, you can solve it (just put the items next to each other), otherwise you can't.  To deal with the isolation constraint, you can note that the problem with tiles lengths $\ell_1,\dots,\ell_k$ and an isolation constraint is solvable if and only if the problem with tile lengths $\ell_1+1,\dots,\ell_{k-1}+1,\ell_k$ and no isolation constraint is solvable.

The 2-dimensional case (a $m \times n$ grid) looks much harder.  One approach, in practice, might be to use a SAT solver.  Introduce boolean variables $x_{i,j,k,d}$ and $y_{i,j}$, with the intent that $x_{i,j,k,d}=1$ if the $k$th tile starts at location $(i,j)$ on the grid and proceeds in direction $d$, and $y_{i,j}=1$ if location $(i,j)$ is covered by some tile.  Now you can formulate your problem as a set of boolean constraints on the $x$'s and $y$'s, then feed it to an off-the-shelf SAT solver.  You could experiment with this for the parameter sizes that tend to crop up for you in practice and see how well it works.  SAT solvers often work surprisingly well, though there is no guarantee: they are not a silver bullet, and the worst-case running time will remain exponential.  There are many other ways to represent this as a SAT problem, too, so you could try other representations as well to see which tends to work best with existing SAT solvers.

I'm not sure you're going to be able to do much better than this: as FrankW says, for 2-dimensional grids this smells like it might be NP-complete in the general case.