I can't really help but I'd find a way to keep the hood and ditch the UV filter. Yep, that doesn't help.
The filter will offer no protection (other than sealing against weather maybe, do you need that?) It is just another piece of glass to hinder (slightly) the lenses capacity.
Apart from the hood protecting the lens I've found it helps get a nicer contrast when taking a photo. There has to be a reason why they are supplied with the lens.