Org mode - Copy cells from a remote org-table with shifted columns

Question

I want to copy the values of a shifted range of cells from a remote table.
Example:

#+NAME: TBL1
| 1 | 2 | 3 | 4 |
|   |   |   |   |

#+NAME: TBL2
|   | 5 | 6 | 7 | 8 |
|   |   |   |   |   |

The table TBL1 should look like this in the end:

#+NAME: TBL1
| 1 | 2 | 3 | 4 |
| 5 | 6 | 7 | 8 |

I'm currently doing this with a dedicated function for each of 15+ cells, which makes the #+TBLFM: line super long and is not maintainable. An efficient way to accomplish this is by using the lisp function identity:

#+NAME: TBL1
| 1 | 2 | 3 | 4 |
|   | 5 | 6 | 7 |
#+TBLFM: @2$1..@2$4='(identity remote(TBL2, @1$$#))

Problem is, that this function looks for values in the cells @1$1..@1$4. I want to shift the cells to look at to the right (@1$2..@1$5).
This has to be done via the REF value for the remote function, (@1$$#). If I understand the syntax correctly, $$# is pointing to the current column of the cell which is going to be filled with the remote value (e.g. for cell @2$1 in TBL1, $$# becomes $1). So this has to be shifted to the right with something like $$#+1.

What is the correct reference for my example?