This is exactly why I will never dump in this manner. If the coins are gone, you have no recourse. Maybe the bank will take pity on you and give you credit. All you can do is call them and hope.
In my area and experience, you have very limited recourse whether it's counted immediately or sent to be counted. Regardless of how you dump, the most import thing is that the bank and/or vault employees believe you were shorted. They get people constantly telling them they've been shorted. I've contributed to the problem by having them do an audit one time when dumping $2000 in coin at a bank. It came up $200 short. After putting them through the hassle, I went home and found a bag my daughter filled with ~$200 in halves. I'm guessing I'm not the only person that's done this.
If you're at the bank for an instant dump and they believe your coin was counted properly, you will likely never get your coin back. If they believe you, keep good records of individual coin deposits AND do a real audit, you will likely get your money back. Sending coin off feels like you have less control. However, if you keep the bags light and consistent, it will help you avoid shortages. Don't mix denominations. If depositing halves, make every bag $500 instead of $1000, even if you have several thousand to deposit. Another idea is to weigh each bag and write the weight on the bag and the corresponding numbered slip. The importance of light, consistent bags is the employees at the bank and the vault will become accustomed to the consistency of the bags. Light bags limit the opportunity for significant shortages. Each bag is counted separately. You can show a pattern of constancy that will probably be recognized by the employee and fixed before you realize there was even a mistake. If it doesn't get fixed before it hits your account, use you deposit slips, account information, and bag numbers to show the pattern of consistent deposits. Again, it's all about convincing the employees that you were truly shorted.
For the record, I know my thoughts are kind of 'one size fits all'. You may have a connection at a bank or live in a region where things are done differently. YMMV
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