Looks like my iPhone will be staying jailbroken on 9.0.2 if semi-untethered is the only option here.
I've made the comment in the past that I wanted to upgrade to iOS 10 when it was jailbroken because I saw iOS 10 as better than iOS 9. But that comment was based on the assumption that I'd get a fully untethered jailbreak.
I'm not leaving a fully untethered jailbreak for one that isn't.
The problem is, I think even Saurik has said back when 9.3.3 JB was released that due to the safety protocols that Apple has put into place, semi-untethered is what we're likely stuck with going forward. We may be reaching a point where you have to decide if it's worth dealing with.
(I've been stuck stock for long enough now that I've mostly kinda sorta learned to tolerate it, and opted for 10.2 knowing I was shutting myself out of a JB. But now that CallKit is in iOS 10.x.x and I didn't need iBlacklist, I was down to Folder Enhancer as my primary tweak and a bunch of tiny, non critical stuff--not enough for me to live with the nuisance of going semi-untethered.)