Cost Effective SMS Solution from Multiple Unique Numbers

I am building an application to send SMS messages using SNS. This application would be used to send out special discount codes from specific stores.

My understanding is that an origination number would be used as the source of where these messages would come from. We'd want each store to have its own unique number so that if someone subscribes to different stores they wouldn't receive a text from the same number for all store messages if that makes sense.

Would each of these stores need to have their own unique origination number? I've been reading about 10DLC and I'm wondering if this would be the solution. Would I be able to register multiple numbers quickly and cost-effectively using 10DLC? The goal is to quickly add new stores and unique numbers for those stores while still being cost-effective.

Short codes seem to take a very long time to register and are expensive so I don't think this would be a good use case for our application. This is new to me, so if there's some documentation I missed that goes more in-depth on this please let me know.