Hi,
I have been working in R&D more than 15 years for international electronic design companies in NZ and Australia . I have designed and developed many 8/32 bit micro-controller based designs, analogue and digital circuits, schematics & PCB layout as well as high voltage and power electronics designs, RF ,WiFi and Bluetooth, capacitive touch interface, stepper motors, battery management etc.
I have vast experience with low power and discrete transistor circuit design.
Re your project
I have drawn the circuit in Simetrix, could send you results, not sure if I could attached jpeg file at this stage. I do not have LTSpice but potentially could install it or you could redraw the circuit in LT to check functionality from jpeg.
The switching happens ~ 2.85 V but sure it can be tweaked down to 2.7 with adjusting some resistors values. The BOM cost around 1USD plus 5-6 resistors.