several recent rulings on sec 1250 and 1245 have clarified that cost segregated depreciation of non-1250 property and accelerated depreciation taken thanks to the JCTA of 2017 are also able to be fundamentally carried forward in a 1031 exchange. 

I am not a guru or a podcast host, just a resource to help you carry out your plan So basically high priced garbage.

But when it comes to conducting Cost-Segregation studies to “accelerate” the depreciation of a property, can I still “carry over” additional entitlement from, for example, my first tax-year into the following years even if I am not meeting the REPS criteria through STR’s? 

You can attempt to raise from a 506c but it will cost you $25k to get started, then if you did get your first $100k  and you are paying them 10% and you are making 12%, - great you just made $2,000 and that is assuming you were able to fund an entire deal immediately and have zero holding or carrying costs. 

We recommend investors carry a minimum of $1M. 

California carries more risk than Wyoming).The facts show that risk is negligible.

Before you buy, make sure to get the latest rent roll (a breakdown of what tenants are actually paying in rent), the tenant ledger (which shows their payment history—whether they’re paying on time or carrying a balance), and of course, a copy of each lease agreement.Too many investors rely on what the seller says, which often doesn’t match up with what the tenants are doing.

Talk to your CPA / Financial planner about this option as it does carry risk!

Also, do the aggregate losses above any W2 income get carried over to the following year?

There are many benefits to carrying a mortgage.