Hi Jeff, the main complication here seems to be your work history and with that I see two main options that you can do.
1) Wait another year and do a low money down/FHA owner-occupied house hack. I would do this with a 2-4 unit and use the rental income to cover your living expenses.
-or if you want to start in the meantime-
2) I would go with hard money/DSCR lending. I am not sure about your experience with rehabbing, but one option is to BRRRR with hard money and refinance into a DSCR loan, but if you are just looking for turnkey rentals, I would begin with a standard DSCR loan which can usually go up to 80% LTV based on the lender.
You laid out a pretty good framework of these options already, but the main item is your timeline. If you have a property that fits your buy box now, go DSCR, if not, hold out and wait for an owner-occupied home. Getting a DSCR loan before an FHA loan could make the FHA more difficult since it will increase your debt-to-income ratio.
Another thing I suggest is to start working with a lender that works with investors and oftentimes, your lack of work history can be supplemented with other activities. For example, I am looking for an FHA househack right now, but have 6 months of work history, but my 1.5 years as a student will satisfy the rest of the two-year requirement. Ask your lender if the time you spent caring for your father can help you meet those requirements (I doubt it will but its worth asking).