Welcome to BP @Keith T.! Here' my $.02 from a couple hours to your West down I-10.
"Most hard money lenders seem directed towards individuals who cannot obtain conventional loans (for people with no other options). Is this just a misconception on my part"
I have to disagree with that and say that's your misconception. HMLs are a different option. Fast, efficient, and flexible. I'll paraphrase an ancient saying, "he who holds the gold, makes the rules." HMLs have their own rules, some want more information, experience or other things, than others. The best HMLs offer investors the opportunity to operate at high volume and bring a high level of expertise to the table.
"I have no problem getting financed by a traditional bank, so I'm only interested in hard money for the flexibility and speed. Are there any other advantages to hard money that would allow me to compete with full cash offers"
Proven consistency of closing deals with HMLs or otherwise, is the only thing that might allow you to compete with real cash offers. When offers line up, cash is king.
"I've also read advice saying get the deal before finding funding. I work in the finance industry and this seems counterproductive to solid due diligence. Any advice on finding hard money BEFORE having a deal in hand?"
That's a wholesaling strategy, not a buying strategy. I can only expect that your objective is to buy, since you are looking for a lender(s).
"I would like to get some estimated deal sheets so I know what to expect."
What do you mean by deal sheets?
"Do hard money lenders give more favorable terms to borrowers with solid financial history, or is it all about the deal?"
If you are thinking in terms of your FICO score, not so much. Some look at it, some don't. If you are talking about REI experience, definitely. Again, HMLs have their own rules and from one to the next you will find as many unique sets of rules as you'll find HMLs.
Your title to this post mentions private lenders (aka PMLs), and all of the content focuses on HMLs. The terms do get used interchangeably and I think that leads to the misunderstanding that they are one in the same. IMO a PML is someone you know through personal relationship whether its a new acquaintance or a family member who has money to invest. That PML funds your deal(s) at a rate that's better than you can get from HMLs and better than they can get in most other fixed income investment options. The PML might not know very much about REI and they don't need to. But you sure better when you put their money on the line.
HMLs on the other hand, are in the business of acting as lenders to REI. They bring a whole different level of know how to the table and when they reject a deal, you will be wise to take note of any of their observations. They are real REI experts who have maximizing profits and minimizing risks in REI down to a science. That's why I use the terms accordingly.