If I do that though then I pay a premium to open the put/short position in the form of theta and interest respectively. And since my portfolio isn't that big I would end up allocating a sizable percent of it to open short positions on all the stocks I want to exclude. So as far as I can tell, it's considerably more expensive than just not holding those stocks to begin with

What I really want is a way for a company like vanguard to let me purchase something based on an index but in the form of a weighted basket of fractional shares. That why I can keep the same allocation as SPY but hold shares that I can micromanage to "fix" any issues I have with the ETF. Theoretically that should be possible to set up for not very much money since there's no active management on behalf of the fund.

Or, you define your own ETF, maybe initially based on some existing ETF or well known index, and then you can dump arbitrary amounts of money into it - but without actually having to individually buy the shares yourself. Maybe a product like this exists already but I don't know what it's called. I would be willing to pay a higher expense ratio than normal low-cost ETFs charge to use this product, but not as high as a hedge fund (since I am the one actively managing it).