In reply to JohnnyW: We approached EJHut in the afternoon (summer) from Glocknerhaus via the Wiener Hohenweg path and a cold drink in the Salmhutte. This gets you to the south side of the range. From there you climb to the main ridge via Hohenwartkees (not much of a glacier, don't recall any crevasses) and a bit of via ferrata type stuff up to the Hohenwartscharte. Then just traverse the top of the Hofmanskees glaceier beneath Hohenwartkopf and up the Salmkamp to the EJHut. This way you avoid crossing all those glaciers on the north side of the range and though you'd definitely be roped up on the off-chance I would think it's a much safer route crevasse-wise. Do get local advice first though, I was there some years ago and stuff changes.
The normal route is really enjoyable, but do get the earliest start you possibly can to avoid queues at bottlenecks. You're right to leave it til a week day but even still expect to be passing crowds on their way up as you descend. That's how we found it in july in any case.