Your drawing shows D1 as “remove”. That’s fine, but you’ll have no reverse voltage protection.
You’re still talking about a diode though, so I suppose you plan on putting it back… somewhere?
You seem to have it backwards. With the divider attached like a stock 105c of course you need to know the drop across the diode. That’s why it’s accounted for in our existing firmwares! Once you connect the divider to BAT+ you no longer care about drop across the diode.
The reference voltage produced by your ATtiny13A is completely unaffected by D1 - it will always be 1.0v /-0.1v. (yeah, that’s a/-10% tolerance… eww). The voltage coming out of a divider fed directly from BAT + will be whatever the divider ratio dictates.