If you wanted to make certain of getting all of the blood out of the the meat, then I would suggest going with the process used by Jewish people to make meat kosher as they are forbidden from eating meat with blood in it for religious reasons.
That process is basically to soak, dry, salt and then rinsed three times to remove the salt. For a longer description see the sources below.
Jewish law prohibits the consumption of the lifeblood of the animal. All kosher meat and poultry must undergo a special process to remove it. The meat or poultry is soaked in clean water for thirty minutes, then removed to drip dry. After a few minutes of dripping, the meat is salted and left to hang for sixty minutes to further draw out any remaining blood. After sixty minutes of salting, the meat is washed three times in cold, clean water to remove any remaining salt.
A bird should be placed with its open cavity downward so that the liquid drains off as it is koshering, and similarly, a piece of meat with a cavity, such as an unboned brisket, should be placed with its cavity draining downward. One may stack meat that one is koshering as high as one wants, as long as the liquid can drain off the meat properly. After the salting is complete, the meat is rinsed thoroughly in order to wash away all the blood and salt. The poskim instruct that one should rinse the meat three times
On the other I have eaten lots of elk meat where we soaked the meat and washed it to get almost all of the blood out and remove more during the cutting and packaging process, and having some blood still in it really isn't a problem.