I haven't seen it in a while, but I'm pretty sure a strict interpretation of ESB allows Han to fix the hyperdrive before arriving at Bespin. IIRC, some kind of power coupler was busted, and they started to replace it while in the space slug. Then they got chased out, and latched onto Avenger. After Avenger dumped her garbage and went to lightspeed, the Falcon cleared the debris field at sublight. The next time we see the Falcon, she's at Bespin.

Emergency repairs to the hyperdrive could've been made after we see the Falcon "floating away with the rest of the garbage." On Cloud City, Lando asks what's wrong with the Falcon, and Han just says, "Hyperdrive." He doesn't say the drive is completely broken, just that there's something wrong with it.

The interstellar sublight hypothesis might work if the stars were in the Core or the Deep Core*, but most EU material suggests the Core is heavily populated and the Deep Core is devoid of human life except for some military outposts and Palpatine's Berchtesgaden.

But the trip from Hoth to Anoat is still problematic.

* According to This source, there are 100 stars per cubic parsec in the core of the Milky Way. That means the mean distance between stars is 0.7 light years.** But the galactic core is not the friendly kind of place where Tauntauns and Wampas can evolve ... it's got radiation, and occasional bursts of energy that make the Death Star's superlaser look like a trickle.

** My math is probably wrong.