Return Text From Left-hand Side Of Ragged Array Where Entry Found

I've been given a spreadsheet that is poorly constructed but I'm not allowed to alter.

The layout is:
Box Name Box Date ID1 ID2 ID3 ....
Where there is not a fixed number of IDs in each box
(There are five different sheets so I'll have some fun concatenating results)

Given a list of IDs I need to return the box name and box date that the ID's file sits in. The spreadsheet has blanks everywhere and the numbers contained in rows are non-consecutive and smaller values can appear later in a column than larger ones.

I think I need some combination of index, offset and maybe sumproduct? TBH, I avoid sumproducts like the plague, preferring to utilise sumifs and dynamic named ranges since this improves clarity so I'm basically a newb at them.

Any skeleton framework that you think would work to return the text values for the LHS where the number could be anywhere? Once I can see a rough example I should be able to get to grips with the logic and wrangle it into the necessary solution.