We are required to give two days notice prior to entry, except in case of an emergency.

If the former I'd look for anything that could be a true emergency or safety issues and address those.

Evictions, damaged properties, and late night “emergency” calls about the toilet running are just a part of the REI game.

Your lease should prohibit changing any locks so that you don't have emergency access.

I examined the tenant's lease application closely and then called the employer, and I was notified that he was not found in the system as an employee.I called the realtor to report all this, I requested vacant possession of my property, and listed the following concerns - Falsification of information to obtain the lease, Forged documentation of employment and pay stub, non payment of rent (he is owing some money from the last rental payment due to not setting up rental payment through AVAIL platform and he made payment with money order one of which I could not cash as he wrote his name on PAYEE section), Failure to provide renters certificate of insurance in his name, Failure to provide utility contracts in your name, Using water from start of lease to date under my name - City of Houston water bill in my name and bill remains unpaid, Water leakage and damage to the property (extent of damage still to be assessed, Unpaid invoice for the cost of emergency work to stop the leak and fix the ceiling in the kitchen, the grass is overgrown and the property was unkempt when we visited last week to inspect the work on the water leak. 

This may not be the type of money you're trying to solve for, but over the past several years I've been gradually shifting a portion of my household emergency fund from bank accounts into I Bonds from the U.S.

It is not a 9-5 job and there will be nights and weekends involved, pending tenant issues and maintenance emergencies. 

I worry that I won't be able to consistently afford a mortgage if I don't have a sunk fund/emergency fund. 

You want a lockbox anyway in case of emergency or vacancy.

-Pool Maintenance (monthly maintenance check-ups and on-call service for emergencies)-Home Cleaners (familiar with scheduling process on STRs)-Photographers (experience in STR photography, aerial capabilities)-Handyman/Contractors (small repairs/updates, on-call service for emergencies)Open to any and all recommendations, thanks all!