Sounds like a safer option to me, as with only a single plane I'm guessing you don't have that much experience using it for cabinetmaking, should say tearout be of concern for one, it could pull out chunks as deep as you intend to go down if the wood is like iroko.
This is a hump in the middle isn't it, and not a dip?
If a dip then simply shimming might be well worth it
Seeing as it's timber, it's likely thicker than this top, and only needing a single point
under the middle.
View attachment 133106
But it sounds the opposite case
I question what you have used to make such an assertion, and am guessing you have a decent enough straight edge
I only bought one recently as I kept using my long stock up.
The edges can be flipped around or over instead, and should give one some sort of an idea of flatness, say should both decide to move in the same banana fashion,
then flipping
one around would make this extremely obvious.
(doubling the error)
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View attachment 133108
But I needed to test it first
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Tools involved
Long plane is much easier, and likely a good understanding of the cap iron.
A calipers, not for reading measurements, i.e could be done blindfolded, you can feel a lot better than you can see, on even the cheapest thing for a tenner in the middle isle.
I like the non digital ones like below.
View attachment 133109
And a long reach lamp for the job.
These ones were made in Italy is the sticker is to be believed, and seem to be hard to find, should none secondhand about then seemingly slightly smaller ones for a tenner
are available if you look for "territal" lamps, in eikeas warehouse.
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May seem fancy, shoot me down, but I doubt anyone would think this kit is
that over the top financially wise, and is stuff that one would use everyday.
Tenner for the lamp, which is absolutely nessecairy anyway.
Fancy calipers probably twice that, should one not have a cheaper one knocking about.
A pencil gauge would get one there but slower.
A long plane makes this easier, but not necessary, just have to be more careful.
Checking eliminates as much need for an only somewhat trustworthy tool,
as in, if one isn't used to using hand planes, it ain't just a case of a hand plane making things automatically flat, no matter the length.
David Charlesworth's teachings is just about the best info you will find regarding
working to fine tolerances.
All the best
Tom