Unfortunately, quality shelving that can take the weight of LPs isn’t cheap.
Several years ago we did a whole home renovation and we used California Closets to do custom built-ins in all of the closets in our home. I had them design built-in record shelves in the closet in my music room. My LP storage system is 5 levels high. Their design also included a pull out shelf for my record cleaning machine, which has worked out well. I honestly don’t recall what it cost at the time, but I don’t think it was as much as $7000, although it could be today. It might be worth giving them a call to get an estimate. Despite their name, they do out-of-closet storage systems as well.
Another option that I’ve looked into for book and LP storage is the Vitsoe 606 Universal Shelving System. It’s a legendary system that is very flexible and very high quality. It’s not exactly cheap, but I think you could do something like you’ve described for a lot less than $7K. Their web site has a ton of pictures of existing installations, many of which show some pretty high-end audio gear too (see the Well Tempered and Kuzma turntables and Naim gear in the image below).
The shelving is made in the UK and they sell direct to the consumer. Everyone gets the same price, there is no discount for going through a designer. They have a free design service that will work with you to create a custom solution for your application. All of the pieces of the system and prices are on their web site and there’s an online builder that you can play with too. I’m seriously considering it for book storage, and maybe some additional LP storage as well.
Hope that helps.