I apologize for the late reply, but I'm stuck with a crazy work schedule recently.
The recipe basically looks OK, although for a 1 gallon mash tun I would be worried about 4.25 lbs total of grain fitting and actually extracting the sugars. One thing you can undoubtedly cut is the cara-pils, which most suppliers actually add a bit already to the LME usually, and the additional protein from the wheat will give it a solid body anyway.
I would also recommend maybe switching all or part of your white wheat to wheat DME (liquid would also work) as that will be easier for you to work with, and I don't feel that using the malt in a partial mash like this is going to make a massive difference in the resulting flavor and mouthfeel. Maybe .5 - 1 lb of malt and make up the difference in extract.
Regarding the IBUs, that is probably due to vessel sizing or a similar issue if I had to guess, although you may also have lower alpha acid content in your recipe than what I had in my hops. One of the benefits of using extract, though, is that you can stagger the extract additions in the recipe, putting maybe half of the extract in at the beginning, and half closer to the end (maybe 15-20 minutes left in the boil). This will lower the effective gravity during the boil which will increase hops utilization, increasing the IBUs. Of course, you can also increase the hops addition. In my recipe I am typically shooting for about 17-18 IBUs, although anything from 15-20 should be fine.
I have made this beer with US-05, and it still tastes great although it doesn't quite have the same fruitiness. The S-04 will finish higher (that is a known characteristic) which is one of the reasons I use a lower mash temp in the recipe. If you are dealing with liquid extract in particular, your recipe is almost guaranteed to finish higher since LME, at least in my experience, tends to have a more dextrinous wort than you can produce using AG and a lower mash temp. One way to handle that is by using DME for all or part of the extract, which tends to ferment out better in my experience. Another option is to sub a small portion of the grain bill with simple sugars, or to add a bit of simple syrup solution after fermentation finishes, which will effectively lower your FG.
With S-04 in particular, another strategy you can use is to (gently) stir it up a few times per day to keep the yeast in suspension a bit longer, as that strain tends to drop out quickly and flocculates extremely well creating a super-tight cake. Once it gets into that cake, it's pretty much done.
Hope this helps. Please feel free to ping me with questions, although my schedule for the next week or so is going to be pretty hectic.