If your parents own it and rent to you it is not owner occupied.

There is certainly an opportunity cost associated with holding the property, but if you can't find any opportunities to invest in at this moment, you might as well keep your money working for you. 

I am going to purposefully withhold some detailed information on the mechanics of how to do this, for obvious reasons, but yes I have gone through this before and am speaking from 1st hand knowledge. 

I'm targeting a 3+ bed home to rent out with a granny unit where I will live (or rent out a room at my parents' for that matter).

That is a conversation to have with your CPA and attorney.You don't necessarily need to change CPAs, but you should make sure yours is comfortable with reporting the 1031 at the federal level, reporting the 1031 to CA in the year of exchange and thereafter, Sec 1446 withholding, FDAP/ECI considerations, and filing your 1040NRs and any applicable individual state returns.

Is there any way my parents could possibly back home could assist me with this? 

And move into my parents vacation home for awhile?

If a parent or someone else over the age of 18 is willing to be your "partner" and sign for you then you're good.

It has been a month but the situation changed, my elderly parents need to move in with us and need a bigger home (covid, sickness, financial, other reasons).

I would like to know if you or anyone you know can help me with services to create a flyer, pdf, or any other ideas you would have to help me get exposure for my parents property before it goes on the market with the people around me and beyond.