We have basically been using the technique described in:
Minoletti, F., Hermoso, M. & Gressier, V. Separation of sedimentary micron-sized particles for palaeoceanography and calcareous nannoplankton biogeochemistry. Nat. Protoc. 4, 14–24 (2008).
In summery: desegregate the sample by putting it, with a small quantity of DI water, into a beaker and hold beaker in an ultrasonic bath. Our samples were very soft so they diddnt need anything more than that and it took seconds to desegregate. (similar age samples to yours, IODP).
Pass the suspended sample through 63 and 46µm sieves and then a 20 µm palynology mesh and then cascade filter (in ultrasonic bath) using laser etched polycarbonate membranes at 12, 10, 8, 5 and 3 µm. (from 3 µm below is basically clay and nano fragments). We concentrated on the 12, 10, 8 and 5 fractions for nannos.
We didn't have a problem with using DI water (for geochem work). However, I know others prefer to not use DI water and also champion the use of a settling technique: e.g.
Bolton, C., Stoll, H. & Mendez‐Vicente, A. Vital effects in coccolith calcite: Cenozoic climate-pCO2 drove the diversity of carbon acquisition strategies in coccolithophores? Paleoceanography 27, 1–16 (2012).