Will this extension work for our needs?

Hi Akiva, 
Thanks for your interest in our migration tool. 
We’d like to answer your questions below. 

We started migration in a project using standard migration tools. 

You need to start a new Magento 2 instance and install our migration tool to avoid unexpected conflict with Magento default migration tool that you’ve used before. 

Can we begin using the migration pro tool to migrate only the catalog and customer for a final migration?

You can migrate part of the data like customer, however, however it still needs to migrate related data portion, depending on which data objects you need. For instance: 
To migrate Customers, you need to migrate steps:
Step 1 (Database Settings)
Step 2 (Migrate Sites, Stores)
Step 6 (Migrate Customers)
To migrate Sales data, you need to migrate steps:
Step 1 (Database Settings)
Step 2 (Migrate Sites, Stores)
Step 3 (Migrate Attributes)
Step 4 (Migrate Categories)
Step 5 (Migrate Products)
Step 6 (Migrate Customers)
Step 7 (Migrate Sales)

In other words, is this extension only meant to be used from start to finish, or can we switch in the middle of project?

As explained above, you need to start migrating using our migration tool from the ground up. 
 
Hope that helps. 
PS. You can check out a few case studies below to learn more about our Pro version: 

-- Migrating 15,000+ Sales Orders to Magento 2 Using UB Data Migration Pro
-- We did use the Pro version ourself to help Winetasting.com – Migrate 382,047 customer entities to Magento 2
-- And this case study as well -- Freelaunch.nl used UB Data Migration Pro to migrate 230,000 products to Magento 2
-- Case Study: Successful Magento 2 Data Migration for Kwaaijongens.nl

 
Regards,
Ubertheme team