It so hard to judge tone and context on the internet, but I'm wondering if maybe there are other issues at play here. Someone getting "furious" or "chewing out" in a conversation about a storage unit or a 4 month shift in pay off date seems pretty unhealthy. And separating finances, especially in the face of that dynamic, seems to perhaps be moving in a somewhat unfortunate direction. Just throwing this out there to see if it sticks for you, but if you think there's something to it, consider spending money on some counseling together, perhaps.
That said, go to the storage unit, and get rid of anything in that there is yours. If it means enough to keep, find a place for it in the house (even if that means getting rid of something of yours in the house). If not, toss it. In the end, maybe you can get a smaller storage unit. If not, you've still lightened your load. But perhaps she will be inspired. It still seems like you are pushing some of this change in her direction, when you probably need to be doing as much of it as possible yourself. Don't nag (encourage, whatever) her about her stuff. Purge yours. Then, if it all fits in a smaller unit, ask her if she' okay with downsizing. Or, if it would all fit in the shed you've already built, ask if she's okay with you moving what's left there. But first you purge your things and spend your time building a shed and don't pressure her at all.
This is a change *YOU* want to make. It may make all the sense in the world to you, but you are the one wanting to change the status quo. So from her perspective, you are basically changing the rules of daily life, and expecting her to follow the new rule book when she preferred the old one. Would she get "furious" if you just built a damn shed in your spare time? If you moved the things you use in the garage into the shed? If you went through your stuff in the storage unit? If you brought your remaining stuff from the storage unit into the shed or the newly gained space in the garage? Stop trying to get her to do these actions with her things, and do them with yours and on your own to the extent possible. Stop even talking to her about it. When you come across a filthy, stained piece of art from the when the kids were little or something that looks like trash but essentially belongs to her, don't ask her if you can throw it out. That will hopefully come later. For now, do what you can with the things that are yours to control.
And I love the suggestion, if and when it is time to again broach the subject of getting rid of or downsizing the storage shed, of suggesting you use half of the money saved in one year for a weekend away or a shopping spree for her, or whatever she values. Sure, it would be better to save all of it (or put it all toward debt), but that's not how you get a very reluctant, spendypants spouse on board. You have to show her the benefit, and it seems like a spreadsheet showing her that you can retire 7 months earlier (still years away) without a storage shed doesn't resonate with her, but a day at the spa or a weekend at a beach house might.