Answer: So far, so good. I think you've done the lion's share of work in your lawn renovation project. If you have no objection to using chemicals, I'd suggest you spray glyphosate (Round-Up) over the lawn area to kill any existing St. Augustine and any seeds that might be there. Wait 2-3 weeks for the chemical to dissapate and then spread some organic matter over the area and broadcast your bermuda seed.
Grass seed won't germinate until late April or May so you have plenty of time. Temperatures have to be consistently above 70 degrees to get the soil temperature warm enough for the seeds to germinate. (otherwise you'll just be wasting seed) In late March or early April I would get a load of compost (not top soil) and spread it, then broadcast your seed.
Best wishes with your new lawn!
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