Think in terms of transmission line segments. You want constant-loss TLs to get the power absorption, then whatever's left at the end is your output tap.
A 7850 ohm TL will be very high aspect ratio indeed. Enough so that, even with a very thin resistance wire (but still big enough to handle what little power it needs to), you won't be able to get an aspect ratio that large without encountering higher modes in that space.
So yeah, staged is a good idea.
Even better, do, say, 3 then 23.5 then 23.5dB, so the first stage absorbs half the power, second absorbs almost all the rest, and the final stage can be reasonable. Unfortunately this won't use any resistors you have...
Tim