Shopify Tag Page Advanced Sorting

Our Shopify site relies on tag pages instead of the standard and more customizable collection pages. We're looking to find a way to sort the products in the collections using a more algorithmic approach than “best selling”, “newest”, A-Z, Z-A that are currently the only options. There are many apps that allow for this type of manual sorting based on a mixture of metrics like sales, word associations, newness, click data, bought together, and so on, but they only work for actual collections, not tag pages. 

We'd like to come up with a creative solution to this that we can sort in a similar way, and that does not use javascript to create the grid of t-shirts. It seems there will be limited options to do this, but think there may be a way to do this with an external desktop app that does the processing of data & sorting every so often, but exports to metafields to store the product info needed to make the grid of t-shirts. 

One thing to consider can be seen on the following 3 Donald Trump T-Shirt collections:
https://chummytees.com/collections/all/trump-t-shirts
https://chummytees.com/collections/all/trump-2024-t-shirts
https://chummytees.com/collections/all/donald-trump-t-shirts

They are relatively similar in which Trump t-shirts are shown, but they are indeed different and don't include all the same designs. We have many similar “collections” where products are similar. These pages would need to remain different so we aren't showing the same Trump tees on each collection. Ideally, we could even show t-shirts that are not even tagged with these tags, but are extremely likely to be bought by the same people who buy the original tagged items. 

This is a pretty unique request, but our ability to sort these pages is crucial to increasing sales. We're open to ideas not mentioned here, but cannot move these pages to actual collection pages.