The decision you have to take is 'is it worth continuing to use this fleece for this project?' You could use the neppy fleece for a bulky yarn, and start again for the fine yarn, with a very carefully chosen fleece, maybe using just the shoulder wool. So far I have only dyed fleece in a microwave before it's spun. Otherwise I would wait to dye until after spinning, if there is any doubt about the success of dyeing that particular fleece unspun.
Was this fleece handshorn or roo'd? If it was machine shorn, then the neps could be the result of new spring growth being included in the shorn fleece. I hate neps. I once had 5 beautiful white Shetland fleeces scoured and carded by a small processor and received back a large sack of pretty much unusable neppy fibre
If you decide to persevere using combs or carder, as Bionic says, whether you can use combs depends on if your staple is long enough. Unless it's under 3" then it should be combable, although you lose a fair part of the total weight with combs. I don't know if they still sell long-toothed hair combs, but they would be very cheap for a trial. Metal dog combs would give some idea too, before you decide whether to invest.