I would not use bipolar power transistors in a push-pull configuration period! (many hidden problems to the inexperienced, especially at high current levels)
I would not use 50/60 Hz inverter transformers. (too bulky)
The 4047 would be last on my list of choices. (hate RC timing constants, prefer XTAL)
It would we a different design all together. (HF switching)
I would use opamps only for feedback, protection and regulation functions and not for
drivers.
I am saying this based on my experience of designing a commercial 5kW UPS for one of my previous employers.
I designed some 400Hz inverters for aviation applications in the 70's using bipolars but using proper precautions like using clever base drive circuitry, baker clamps, device desaturation detection, transformer saturation detection etc. Today most things are much easier and safer using power mosfets and dedicated drivers.