How can I speed up the compile / publish time of Flash IDE projects

You could try to split up your application to separate .swf files and then load them from the main movie.

Also it might be worth to look at your environment. Maybe your machine is running out of RAM, you are using an network drive or your hard disk is encrypted.

Also if the application is getting that big, is Flash really the right technology?

Uncheck "Warnings Mode" in File > Publish Settings > Actionscript 3.0 Settings. This makes a huge difference. In a recent project I reduced my compile time from 1 min 20 sec down to 7 secs! Yeah, I was astonished too.

For me it turned out that I removed the character filter on my text fields. This seems innocuous, but in fact it has to embed every fracking glyph it can which resulted in a huge swf file that took forever to compile! Anyhow, definitely check that - I think a lot of people could easily overlook this.

In Flash CS4, disabling Warnings Mode speeds up code compilation by about 30% (still quite slow). Strict Mode also, but I'm not sure to what extent.

As for library assets, the optimal speed is achieved by setting JPEGs to "Use imported JPEG data" and PNGs/GIFs as "Loosless PNG/GIF". As for sounds, I'm not 100% sure, but I think that ADPCM/mono-to-stereo/5kHz/2bit was the fastest. The [Embed] tag might also help (it doesn't do any convertion) but it includes quite a bit of Flex code.

And as a tip, in Flash CS4 you can batch select assets in the library and apply settings, so you can easily set the optimal speed settings while on development and then change them for deploy.