I've just done an "exploration" trip in an Asp myself. The class 4 drive is definitely the way to go. You have to refuel almost every jump, but that generally only takes 2 or 3 days and you more than make that up with the time you save by being able to jump much further. I had 19 tonnes for fuel, and a full jump is 16 tonnes. I had pretty much minimal equipment, but I think I had a single shield generator, an ECM and a superfluous autopilot, so could have clawed back another 7 tonnes or so without those. I feel like at least the shield generator is needed though, since there's no opportunity to repair hull damage. I have no idea why I took the autopilot, I can only imagine I couldn't get it removed at the system I set off from, or I just switched my brain off at the time.
But still, I made a round trip out to 290 light years and back, so about 580 in total, in about 10 months. And that was with a couple of sightseeing stops and planetary landings and things both ways. From Ethceda (12,6), it's only about 260 light years to the Pleiades, so there's plenty of time to make your way there AND back if you want to.