Tucking stakes is my least favorite part of weaving a flat reed basket (I think that's why my favorite style of weaving is round reed, the rims are so much fun!).
In case you feel the same way. here are some tips and tools to make it go faster.
Cutting the inside stakes flush with the last row of weaving (the rim row).
If the stakes are dry, rewet all stakes with a wet (but not dripping) sponge. You want to rewet the stakes but not drip or spray water all over your basket, especially if you have wooden handles or bases.
Use the Plato Shear to cut off the stakes. If the stake is wide, cut 1/2 way through the stake, bend the cut part back and cut the rest of the way through.