Do you think it’s best to use them or can I handle these transactions on my own? 

It sounds like you’re handling this situation thoughtfully, and you're right to question the validity of the HOA’s stance.

So, the first question they usually ask a PMC is about fees - instead of asking about services and HOW those services are executed.EXAMPLE: PMC states they will handle tenant screening – what does that specifically mean?

Start doing category 1 items right away, provide notice and do category 2 as soon as you can and finally prepare and get ready to initiate category 3 items based on your ability to handle them. 

You have to handle the leads well.

.- Have discovered owners with lapsed ploicies they thought previous PMC was handling.- Also found terrible policies that owners had, that they didn't understand.4) Utilities: We check that all utilities are properly set up and cofirm or enroll in any Auto-Transfer of Service programs to avoid no heat during winter leading to frozen pipes.- Dealing with a very upset new owner client right now that previous PMC didn't handle the water account properly.

I'd also have a hard move out date along with the lawyers (or whoever handles your closing-I'm in Canada where it isn't always the same as the US) holding back a large enough amount to get her to move out on time and leave the place in good condition.

This is exactly the sort of thing they would handle for you seamlessly.

Yes, rents have been decreasing in certain areas, and it’s definitely having an impact on how landlords are handling tenant approvals.

Find a good agent that you like and let them handle it for you!