I spent some time recalculating our savings rate to account for some of my
previous concerns in the best way I could think of.
For example, I added to our gross income 401k and HSA and pension matching funds, all of the rents we receive, and a few other little odds and ends that I don't normally think of as "income", but didn't include investment returns. This makes our total income look ridiculously high. I added to savings the principal and postive cashflow portion of all mortgages, all 401k and HSA and pension contributions, and our roths and taxable accounts. Taxes I greatly simplifed to just my portion (not employer's match of) OASDI, medicare, and federal income tax. We don't pay state tax.
Property taxes were one sticking point. Despite the OP asking to exclude them, I just cannot fathom how to account for property taxes as anything other than an expense. I pay them every year. I could pay less if I moved. They aren't proportional to my income. They are not savings. They are voluntary spending, just like groceries and utilities, so I left them lumped in with expenses.
All of this accounting dramatically changes the picture of our finances, but surprisingly makes very little difference in our overall savings rate, which still hovers around 65%. That seems less impressive when you add up the number of dollars in the remaining 35%, which seems about double what I consider my family to actually spend in a year, but then I have to remember that this 35% also includes taxes and mortgage interest on multiple properties, large child care bills that will drop out in retirement, and other weirdness like medical insurance that I normally don't see.
One interesting thing to note is that for people who are heavily invested in real estate, this kind of accounting makes their savings rate primarily determined by where they are in the amortization schedule of their mortgages. A bunch of young mortgages would show high interest and low principal payments, and thus a low savings rate. A bunch of late mortgages would show mostly principal and very little interest payments, showing a much higher savings rate. And that's true for identical payments over the life of the mortgage, which seems kind of bogus to me.