This seems like the easiest way, to just write yourself a check and deposit it your own account.

The mess that we took over was substantial - no leases, little contact info, and no idea what the security deposits were.

I have been happy with both apartments.com and zillow, however they both take some time to deposit rents.

For example, I'm assuming that I don't need to notify the tenant before we come in to the common areas for maintenance.2) As far as I can see, the previous landlord was not paying the tenants simple interest on their security deposit when they checked out.

Some places you can buy a property with a deposit and pay for it within 30 days.  

Often times there can also be implications for rates and products depending on the deposits you have with a specific institution as well.

My question is can I secure a deposit/holding fee from them 2 months out to hold the property for them. 

We have and we just do a double deposit. 

So if lending falls through, you have to pay cash or waive your right to getting your escrow deposit back. 

You also have to realize that even if you are not using the entire heloc limit "Some" underwriters still calculate the Maximum payment into consideration.There are some ways to pull money out of a Heloc and deposit it into a savings/checking account prior to application to satisfy the PITI reserve requirements.