I'm going against some of the things you suggested here but one possibility I've found that could work is the following (where each space must be filled by a unique digit between 1 and 9)
Framing it in this way makes it look like a single equation. I checked using a computer and this has exactly two solutions
which look like yours but with the end pairs ...
The number you're looking for is:
The three digit number $x$ is:
The two, two digit numbers ($y$ and $z$) are:
The one digit number is:
Concatenating these together gives us:
Note: I brute forced my answer since the no-computers tag wasn’t specified.