Help with OFFSET, or an alternative

Hello. This is my issue: I need to made some inventories for a range of suites, and I was provided with a table to input the data; tables for each room are the same; they have several sections (in attached example, Hallway, Living Room and Bedroom), and there are items within each section; some items are the same for different sections (for example, doors), and some items are unique (for example, beds obviosly exist only within Bedroom section).

I need to summarize each item in each section.

If sections were in separate column, it would be easy, via SUMIFS (as shown in columns J to R in attached example) or SUMPRODUCT or probably more ways. But, they are not in a separate column, but only within a header row of each section, and I am not allowed to change it.

Is there a solution to this issue? I tried OFFSET, but didn't manage to get it working...

Of course, easy solution is to summarize each cell, but there is a hundreds of suites and a dozen of sections (not only 3 as shown in attachment), so it is physical and error-prone work, to type SUM and then find the appropriate item for each suite and section and click it, a thousand of times. Surely, Excel can provide easier solution? No macros, please, I want formula.

Thanks in advance!

Thank you for the efforts, guys! This solution with named ranges seems elegant, but problem is that there is a couple of hundreds of suites, which means a thousand of ranges, so I'm afraid it's not simpler way... Anyhow, it seems I will have to go with auxiliary columns, nevermind.

Thanks for taking time to adjust the spreadsheet and reply!