As a programmer turned DBA, I have two comments.

First, your "Invoke SQL" subroutine should take an existing connection and a query. I don't know how PowerShell does with connection pooling, but recreating a connection for every index you move can slow things down if your connection aren't being pooled for some reason. Ideally, since you know you're doing a load of work all at once, you'd want to create a single connection to the server and re-use it for each sql statement to that server.

Secondly, have your "Invoke SQL" routine return the dataset instead of the first table. This makes your script a little more flexible and a little more bulletproof. If that first table doesn't exist you can record an error rather than just waiting for the script to go "Boom!".