Help me pitch a CRM to my boss

HI r/crm, I'm part of a project at my company where we are trying help our sales department to gauge their productivity and see if we can redistribute work amongst the sales associates. But the biggest problem is that there's a huge amount of disconnect amongst the data on the sales associates, their leads, contracts, what clients they oversee and for what region, and the like.

Currently the sales department is handling all this via excel spreadsheets and a non standardized process. There aren't any known CRMs in place for them to my knowledge, and this is the biggest hurdle we have to jump through before we can do any sort of productivity analysis.

I work at a very large company with 80000+ employees and I estimate the sales department we are working with to be at least 700 people. (I could be lowballing this number, because I was only counting business development/customer sales managers so I don't know if those people manage lower level sales associates) and from my understanding their main source of clientele are grocery and retail chains and stores.

My boss is trying to have us develop an in house solution to aggregate and validate the data we got from sales, throwing out the lingo that we will automate and take ownership of this "CRM" we made ourselves. But neither me nor the other people including my boss on this project are technically proficient enough nor have enough time to devote towards working on this.

I would like to push the idea of getting a CRM, or at least entertain a demo or a trial of some sort for the sales team. I was looking at Salesforce because of how robust it is, or maybe Hubspot or Pipedrive. Budget would most likely be the issue since my entire company is extremely stingy with money.

Do you guys have any experience with convincing your bosses on getting CRMs?