I remember seeing the Self Employed launch from inside the company. It was somewhat of a skunkworks project from 3 engineers and they got a lot of internal PR for creatively targeting the gig worker market. I guess the plan was to eventually branch out to other self employed people, but the initial motivation was Uber drivers and such rather than small business owners, because that would cannibalize the QuickBooks Online market. It doesn't sound like much has changed in the 5 years since I left. It sounds like you fall a bit in between their product offerings, but I wouldn't count on them handling all your needs because they'd rather people like you just moved to their full QBO product.

I also remember attending a session that Intuit offered on the competitor landscape and being quite surprised that Wave wasn't covered. Intuit just doesn't take them seriously, but their products, to me, seem better than just about every competitor covered in the session, including Xero. They've got a self-employed offering [0] that might be worth experimenting with since you can start for free and only pay when you need the premium features.

[0] https://www.waveapps.com/accounting/self-employed