We use a loan servicing software that has a monthly subscription. 

The differences between most software is subtle and may be how they bill for their service, support their product, or the process to use those features.

Mozeo is a fairly user-friendly software, and very affordable.

@Julie Doke: Industry specific software speaks to you and you can easily relate it to your day to day process.

Quote from @Patrick Roberts: Echoing what Chris said - use a third party servicer.

The servicers have to send notices 15 days prior to the transfer, but the new servicer is required by law to honor any payments made to the old servicer for 60 days.

Nathan above gave some good software recommendations, any of which would probably work well.

Quote from @Ryan Konen: You are correct that comping software like Privy, Propwire, and Propstream primarily rely on public records for their data, such as county assessor records, MLS feeds, and sometimes 3rd party aggregators.

Service seems useful.

We use a third party servicer to do all of this - much easier and when starting just tracked payments in wuickbooks as servicer tracked everything else