Unsolved Using NoIndex Tag instead of 410 Gone Code on Discontinued products?

[BakeryTech]

Hello everyone, I am very new to SEO and I wanted to get some input & second opinions on a workaround I am planning to implement on our Shopify store. Any suggestions, thoughts, or insight you have are welcome & appreciated!

For those who aren't aware, Shopify as a platform doesn't allow us to send a 410 Gone Code/Error under any circumstance. When you delete or archive a product/page, it becomes unavailable on the storefront. Unfortunately, the only thing Shopify natively allows me to do is set up a 301 redirect. So when we are forced to discontinue a product, customers currently get a 404 error when trying to go to that old URL.

My planned workaround is to automatically detect when a product has been discontinued and add the NoIndex meta tag to the product page. The product page will stay up but be unavailable for purchase. I am also adjusting the LD+JSON to list the products availability as Discontinued instead of InStock/OutOfStock.
Then I let the page sit for a few months so that crawlers have a chance to recrawl and remove the page from their indexes. I think that is how that works?
Once 3 or 6 months have passed, I plan on archiving the product followed by setting up a 301 redirect pointing to our internal search results page. The redirect will send the to search with a query aimed towards similar products. That should prevent people with open tabs, bookmarks and direct links to that page from receiving a 404 error.

I do have Google Search Console setup and integrated with our site, but manually telling google to remove a page obviously only impacts their index.

Will this work the way I think it will?
Will search engines remove the page from their indexes if I add the NoIndex meta tag after they have already been index?
Is there a better way I should implement this?

P.S. For those wondering why I am not disallowing the page URL to the Robots.txt, Shopify won't allow me to call collection or product data from within the template that assembles the Robots.txt. So I can't automatically add product URLs to the list.

[BakeryTech]

@maribailey10 If I could I would, but we very rarely have products similar enough to the discontinued one for that approach to make sense. Hence why I plan on sending them to a search query page.

Occasionally, we are able to immediately replace a discontinued product with a replacement, but that rarely happens.

[maribailey10]

No just try to interlink them to other similar product and edit content accordingly