I would check with a contractor about changing out the fixture - replacing the existing one may not be as affordable as you anticipate, depending on how the "drop down" was constructed.

@Sammie J, if it's not too hard to do, do you think it's a good idea? If not, what would you do?

I would definitely change it out if I had the funds. However, I'd choose a more transitional fixture (the one I can see in the entry and the sputnik are very different in style). If you go with the sputnik, I'd use a regular (not edison) bulb.

As long as you will need to get an electrician and fix the ceiling, I'd center the fixture over the island and add can lights (on dimmers) while you are at it.