Others may have personal experience to share.

The only person willing to lend me money was Paulie—a guy who charged a point a week and always had a baseball bat within arm’s reach.

we can do it not rented but rate will be significantly higher. easier and more cost effective to rent it. unless the bridge money needs to be paid back asap or you need the funds back to buy more, then a cost analysis needs to be done. personally id get it rented at market rent or a touch below if time is a factor. 

Gifting equity in a house may be more trouble than it is worth if you are not near the life-time exclusion1) Potentially having to get the property appraised everytime an equity is gifted2) Having a title company update the title every time3) Exemption of the gift tax return is normally for cash gifts below the annual gift tax exclusion, you may still need to file if you gift non-cash4) If there is partial ownership over several years, having to properly pro-rate certain items such as real estate taxes, mortgage interest and rental income if the property is a rentalBest of luck 

I let the booking expire and figured it was a troll.I then get another request from the same person about a month later for the same dates.

Being a normal person and giving someone a heads up has not bit me, yet.In addition to what the law requires, I always shoot the tenant a heads up either via text, call, or email.If they are mostly responding to email, then shoot them an email.Emojis and gifs work wonders in today's day in age.

That said, here is how I would proceed...For some background, I used to run an STR management company in SATX and we peaked at about 35 properties under management. 

Quote from @Jeffrey Duck: I see no reason to pay an attorney for this, but it's your dime.The current lease was between you and Person B.

Bonus points if you have worked with them and have personal experience.The property is in South Carolina, if that matters. 

if anything then I would set a flat fee to pay them for their service and then if you do find a property that offers buyers agents money, in which almost all I have seen still do...then I would have the title company back out the amount you decided on and the agent gets the remainder of the amount of commission that's left over.