I've read around that one of the reasons for bitcoin's slow adoption is the psychological factor of having "just a few bitcoins."
That's silly. That's like saying there is a psychological factor of having "just a few thousand dollars". Anyone who feels that way, isn't capable of logic and reason. As such, they wouldn't contribute much to the economy anyhow. Eventually, when all they can have is "just a few micro-bitcoin, they may finally see reality and come around.
Hypothetically speaking, would it be possible to simply redefine what a bitcoin is worth? Say, multiply it by 1000 so that a bitcoin becomes what a millibitcoin is currently considered, and therefore, leave the maximum amount of bitcoins at 21 billion with up to 5 decimal places?
Hypothetically speaking? Sure. You can redefine any word in any language if you can get enough people to agree with the new definition. Seems like a pretty silly (and confusing) thing to do though. Perhaps it would be better to just explain to people that there is a brand new crypto-currency available. It is useable everywhere that bitcoin is usable, it is exactly as likely as bitcoin to succeed, and it has all the exact same security and popularity as bitcoin. It is exactly like bitcoin in nearly every way. It even has a permanently fixed exchange rate with bitcoin. This new currency is called a "Millie". You can get exactly 1000 "Millies" for 1 BTC, and you can get exactly 0.001 BTC for 1 "Millie".
The great news about this new currency is that it is much cheaper to buy than bitcoins. At this moment, the exchange rate for BTC at BitStamp is $511.05 per BTC, but you can buy 1 "Millie" for just a bit more than $0.51. If you actually have $511.05 available, you can purchase exactly 1,000 "Millies"!
If people are foolish enough to be upset that they can only own "a few bitcoins", then they are foolish enough to be excited that they can own dozens (or hundreds) of these "Millies" that are just like bitcoins!
What would be advantages and disadvantages to this?
There are no advantages. The disadvantage is massive confusion as some people talk about something costing 0.5 BTC, and nobody can tell if that's "old bitcoins" or "new bitcoins".
Do you think it would even be worth the hassle?
Absolutely not.
These last few questions were mostly just for me to develop a standpoint. But what I really want to get answered is, how feasible is it assuming it needs to be done?
It doesn't need to be done. There is no technical reason that it can't be done. It's exactly as simple as deciding that it would be better to change the names of colors. From now on, the color we have always called "blue" will be known as "red", and the color we have always known as "red" will be known as "blue". Technically, there is no reason that the names can't be changed, but what a mess to try to get every English speaking person in the world to be aware of, and accept the change.