Can a "thin" hard drive be put in a "thick" case?

I've got 2 sad iPods that I am hoping to turn into one working one.

The hard drive works great on my Model# MA002LL which is in a thin case, but the headphone jack will only play one headphone or speaker. I have a SquareTrade warranty on it but they say they can't replicate the problem so won't fix it.

I have a thick case Model# MA147LL that the sound is perfect on, but it gives me the sad iPod logo 90% of the time.

Because I'm trying to go from thin to thick, will the MA002LL hard drive work in the MA147LL case? Are there any weird mods needed to make it work?

I've swapped parts on iPods before so I'm comfortable doing the dirty work, but I want to make sure the parts are compatible before I try.

Thanks!!!