Originally posted by Martowski but am concerned that image quality may not be much better than the kit lenses and/or may fall noticeably lower than what I would get with the DA 35mm 2.4 prime.
I think that's a valid concern. I personally would suggest you buy a prime as soon as possible. DA 35mm, DA 40mm (XS is fairly cheap), DA 50mm f1.8... All of these will be great. Really, there is a big difference and you will not regret it, even if you "lose" some flexibility. You gain a lot more, better low light performance, better rendering, etc.
You already have two kit lenses, no need to buy a third. You should keep the 55-300mm, because even if it doesn't have the best rendering, it is adequate and has great reach. Finding another lens that goes to 300mm and has significantly better IQ will probably cost a lot more. Its always nice to have a tele on hand.