Bash get string between 2 6-digit numbers - string

Question

I have a UTF-8-BOM encoded text file full of lines of which most start with a 6-10-digit (number increases every line) and have a string behind them.
I want to get each of those "lines" (including the number) to process further in my bash script.
It'd be an easy to do by just using a for loop with sed -n '$line\p' but unfortunately some of those strings I need have line breaks as part of them, so I need a way of extracting the string between two 6+ digit numbers (including the first number) which mark a new line.
An example of 3 "lines":
123456\tA random string here
123567\t another string
this time
it goes over
multiple lines
124567\t a normal string again
What I need:
123456\tA random string here
,
123567\t another string
this time
it goes over
multiple lines
and
124567\t a normal string again
A few things:
The strings are not surrounded with "" unfortunately
All numbers the strings contain are <6 digits long, so a >=6 digit number is always the start of a new string line
The number increases, so the number before the string is always lower than the one behind
I'd like to convert all special characters like tabs or line breaks to \t or \n
I need to get the byte length later in the script, a string must keep it's length
I'm still new here, so if I put this in the wrong place or if it was already answered, tell me!

Answer 1

I hope the "UTF-8-BOM encoded" is not a trap.
Here is my proposal if it is not.
bash-3.1$ sed -En '/^[0-9]{6,10}/!{:a;H;n;/^[0-9]{6,10}/!ba;x;s/\n/\\n/g;s/\t/\\t/g;p};/^[0-9]{6,10}/{x;s/\t/\\t/g;1!p;x;h;z;}' input.txt
Output for sample input (with a newline at the end):
123456\tA random string here
123567\t another string\nthis time\nit goes over\nmultiple lines
124567\t a normal string again
I assumed that the relevant 6-10 digits also always are at the start of a line,
otherwise it gets trickier.
Note:
The string length will increase by 1 for each newline \n or tabulator \t;
because the requested "\n" and "\t" are two characters each.