Only upsize enough to make the minimum. I resize the longest side to 5025 and that makes the photo 48.2 MP
I was accepted with one of my photos taken with a 10D 6mp and the 28-135 lens, which is noticeably soft. I did do a little sharpening on that one. Usually I do no sharpening.
Framing the original photo in camera and not cropping (or very, very little) seems to be the key for making sharper and more acceptable images.Had my first rejects last month with a 40D and 100-400 IS USM shot at 100 ISO! The focus point may not have been on the center of the subject, but when I sharpened and re-submitted, minus the one I guess was offending, they were rejected again. I gave up. The original needed to be cropped to about 75% of the original image.
Batch rejections are a dumb idea. One bad photo and all the rest get dumped? Then there are people who will try to sneak a soft one through with a batch of good ones. The other part is, they don't say which photo was the cause! I suspect this is to make review go faster. They spot check and if the batch looks good, they go through.
Upsizing is no secret science and the software I use has varied and doesn't seem to be the problem. Elements 5, and Photoshop CS2 or CS3 are what I'm using now. Point is that as long as you use something and don't have to crop the original much and use bi-cubic on the settings, the re-sizing shouldn't be the cause of the rejections.
I don't shoot RAW when I'm out in the field. I've had ISO 100 and 200 photos accepted. I do make sure I have a tight crop for the selected original, which I find an important factor.
For the pictures that need some editing before saving again, in other words, more than just resize and minor adjustments like Levels and color correction, I open and save as a TIF. Then I make changes and save as a JPG final size. This is just in case I need to make more changes later and don't want the image loss from opening and re-saving a JPG.
I have Lightroom and don't know how to use it properly. (yet?

) That would be my pick for editing because it does processing and saves a new file, leaving the original untouched.
I think most of us who just do photography and not heavy duty art editing would be best off with Lightroom and don't need to waste money buying CS3, or CS4. In fact, Elements does what most photographers need at a very reasonable price.