When resawing on a bandsaw I don't have any problem pulling the
work through to finish the cut. Typically a bandsaw table is
so small you have tohold onto the wood anyhow and I use a
resaw 'fence' that is a vertical post with one corner aligned
with the teeth of the saw. A long fence is more trouble than
help on a bandsaw.

As to the kerf closing on the blade, it won't cause kickback but
it might burn the wood or stall the saw.

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FF