The software "Cozy" should be able to help you out here.

What software/tech would you recommend to get a jumpstart on wholesaling.

What is the best method for an early stage real estate tech startup to get real estate listing data (in the U.S.) in order to to apply it to software and make it public through a web marketplace where users can connect with the listings original listing agent?

We use Buildium (a property management software that I believe BP gives you a discount for) that keeps track of all our financials.

We run most of our leads through our software via text and email and the vast majority of leads do not produce anything. 

If so, is there existing software/programs that would allow my website to two-way sync with other booking sites such as Airbnb and VRBO so when someone books one of my rentals on my website, it automatically updates with Airbnb/VRBO for the sake of taking those days out of the inventory and then the opposite occurs, when someone makes a reservation/booking on Airbnb/VRBO (assuming my properties are listed on those sites), it automatically updates my website with the new booking?

What are your experiences on the various software to best serve this situation?

There is plenty to do, amazing wineries, casinos, live music, theater, great restaurants, and tons of parks.

I'm an actuary/software engineer by trade. 

What software is your favorite?