The solution is easy. You need more ukes. I have my father-in-law's old early 1960s Silvertone/Harmony soprano uke. All solid mahogany. I probably went through three or four sets of strings (Martin crystal, Martin fluorocarbon, a couple sets of Aquilas) before I realized that I didn't have a wolf note on the E string, but that I just needed to let the strings settle in. Before they settle in the E string is annoyingly louder than the other strings if played open, but fine when fretted. So after restringing it with Aquilas and letting it just sit and mellow for a couple of weeks, it sounds great. Balanced, loud, good tone. I also have a Lanikai concert which came with Aquilas and which I haven't changed yet (they probably settled in when it was in the store), and a Mitchell. The Mitchell had Martin crystals on it when I got it and they're not my fave string, so I restrung it with Aquilas. Had a LITTLE bit of the same problem with the E string, but only for a few days. Probably the difference between the solid top on the Silvertone (which is VERY responsive) and the laminated top on the Mitchell.
The strings on all three of my ukes are settled in and life is good.
I should have figured this out early on. I've played classical guitar for decades and would NEVER think of changing out the strings on my three classicals at the same time. It's the nature of nylon strings I think.
More than one uke, stagger string changes so that they're a couple of weeks apart, and you should be ok. Hey, it's a good justification for UAS.
I use a tiny little Planet Waves tuner that is sensitive as hell. Has a zero tolerance policy for sharp or flat. I also had a little trouble with the friction tuners on the Silvertone so I changed to gold-finish, geared Grover tuners from Stew-Mac. Tuning is now VERY accurate and the tuners look just fine.