If they prevent you from making 1 big mistake, the few thousand bucks you pay them would be well worth it.Probably a good idea to pick up the BiggerPockets Rental Property Investing book.

Are there any laws preventing me from using that money to purchase a rental?

It is to prevent the buy and hold investor you see so much of in baltimore. 

I understand the logic behind why people just deduct them as overhead, but technical rules prevent doing so.

This is the reason why LMR is collected to prevent tenants from stiffing a landlord at the last minute.If you can find a replacement tenant for the first of September you can refund her LMR otherwise she is responsible for September rent.

Hopefully you are addressing issue preventatively so you wont really have to use the HELOC while you're low on cash, but it is there for security if you do.

I have actually been on the seller side of this situation, and it is very frustrating when a tenant prevents a showing to a potential buyer.

We still need to go back and do touch up stain on the floors where the movers gouged deep scrapes in the floors, and some carpet cleaning in the common areas that I promised to do for them. 

If the title is clear, what would prevent me from being able to sale the property or take equity out?  

Your absolutely right though, need to get that termite bond and ongoing preventative treatments.