Weakest Link + hardwired = ??

Why not write or call Pro-ject and have them tell you if they can exchange what they have for what you would like? If they do it and it is still under warranty, the warranty should extend to the work they do, shouldn't it? A way of upgrading and gaining some sort of warranty for what was done.

Your post suggests that Pro-ject don't use "half decent" cables to begin with. The cables hard wired in are quite probably very good if Pro-ject has used them, and done their testing and tuning with them.
It's true that the cables from a turntable carry a fairly low level 'fragile' signal, and good IC's will certainly help, but don't automatically reject the cables that came fitted to the TT.

I changed out the really cheap stock RCA connectors on my entry level Project TT (Model 1.2 I believe) w/ some Neutrik NYS373's. ($1.89 from PartsExpress.) What a difference! Good advice from Carl. I don't what model you own, but if it has those inexpensive 35-cent RCA connectors on your cable, consider changing them out. In regards to your second question, yes it will make a difference but I personally won't go overboard on the IC. Bill.