BUT do you think just because something is gifted to you will you be more motivated to let it go below market value?

Usually that just slows them down to train you and watch over you.Find out what someone likes, call it a gift, show you'll do anything to learn.

I am aware of California's Prop 13+58+19 prop tax inheritance evolution and its complexities with LLCs but we are not considering inheritance or parent->child gifting etc.

For example if you wanted to gift $100k to your child to purchase a business, it may be best to make your child manager, with say a 20% interest, while you and or your spouse maintain a 80% interest.  100% of any net income can still be received by your child as manger, or even for just his 20% interest, as profit allocation  need not align with ownership percentage in an LLC.

Sure if you dont have your own 3-5% down payment then yes use DPA if you really want to buy.After going over the pros and cons typically our FTHB'ers or first time home buyers end up getting a gift or bring in their own 1-2% down + 1-3% gift and end up with 3-5% down payment and borrow at regular FHA/conventional rates (avoid the DPA program rates).This is actual experience.

I have recently been gifted my great grandparents home and it's going to be a complete gut and renovate costing approximately 150k.

Keep them updated to reflect seasonal decor or recent upgrades.Offer High-Impact Amenities: Small touches like a coffee maker, fast WiFi, or a thoughtful welcome gift can transform a stay into a memorable experience.Stay Communicative and Proactive: Prompt, friendly communication makes guests feel valued.

Another thought you could just keep the tri-plex and gift them the net income each year...it's basically the same thing without any transferring. 

I don't know much more specifically so ask your CPA about gift taxes (I think she could give you $17k of gift money a year without taxes) or capital gains taxes if/when you want to sell. 

I want to use her equity as a gift for the down payment to avoid capital gain taxes.