Yes, Jzadirune is long. Give the PCs some help in finding the secret entrance to the Malachite Fortress. They can leave J then and get on with things.
If you insist on the training rules, you're going to have problems with Flood Season (long adventure, time critical); Zenith Trajectory (long adventure, somewhat time critical); and Demonskar + Smoking Eye (long adventure, planar travel, can't rest or get home).
I didn't find Drakthar's Way to be overbalanced.
If they're getting their butts kicked by the traps, perhaps they might want to stop opening doors. Jzadirune can be done by using the pulveriser tunnels rather than the trapped doors.
The module was written with the idea that the PC's would be able to level up during a chapter, rather than just between chapters, and it's not just for time considerations: in several of them, they expect the PC's to be a couple levels higher for the final encounter than they were when they started the chapter.
If they're still not going to be able to level up during the adventure, you might want to consider prying open the treasure hoard a bit and letting them have some minor magic items--potions, scrolls, wands with just a few charges left.
Remember, the two main purposes of the entire first half of the campaign are to level the PCs up and to give them some information on what the second half of the campaign is going to be about.
I agree with the others that you will have difficulty with the training option.
Jzadirune took us about 2.5 sessions to go through every room. Jzadirune doesn't really advance the plot at all. Maybe you can switch out another adventure for the Jzadirune part and then go straight from the Locksmith to the Malachite Fortress in Life's Bazaar. that would be more compatible with your rule and maybe not as deadly.
Drakhthar's Way had one character death and was when the goblins jump them on the second map. However, I don't think they have to level in the middle of this to succeed with it.
My group actually did quite well. They had a scout (instead of a rogue) and hit a lot of the traps. The traps aren't exactly that deadly, however. My group are all experienced players and play really good as a team, however. They complement each other and use good tactics. I once had another group go through it and they didn't do too well at all, but that group couldn't spell tactics and tended to be more chaotic neutral (as both characters and as players).
You could interject Drakkar's Way (as it was suggested). Parts of that can be done simultaneously with Life's Bazaar.
One thing I did was to leave the game Greyhawk but add a bit of Eberron into it in that I allow the players Action Points. This gives them a bit of help in making skill checks, saves, and help stabilizing from bleeding to death. I know I have been doing my job correctly for I have been causing my players to burn through their action points quickly.
