I think tablet handwriting is fine. I had some six weeks of down time a while back and took advantage of it to go through the Getty-Dubay book Write Now: the Getty-Dubay Program for Handwriting Success to improve my handwriting legibility. There's a website now https://handwritingsuccess.com/ and for your purposes even more relevant, there's a mobile app. I'm not affiliated, in case you're wondering.

As for disorganization, that's kind of the nature of early notes. There are ways to kind of organize them. One technique I use is writing them on notecards or notecard-sized paper, which I can later shuffle and organize.