Intergration is a slow process...normally. I personally would NEVER put my own cats with the fosters I have until they have had an opportunity to smell each other from under the closed door where the foster cats are.
A good trick is to take a cloth and rub the sides of the cheeks of the new cat and then put the cloth where the other cats can smell the newbie. Also, ensure that the cats do not come into contact with the new one all at once. I recommend to take your mildest mannered cat first to meet the new one. If it goes well supervise the bonding. I normally take my sweet female and put her in with the foster(s). Then move each cat in one at a time over a period of time so that they all get to meet the new cat independantly. All at once can cause fights and the new cat will be overwhelmed.
As you have seven cats, I would say it would take approximately 7 weeks to successfully intergrate all together. If the new cat and another one of your cats bond well, then leave them together in the room so that they 'stick together' when it comes time to open the door and let the new one explore.
Do NOT rush the process. In order to successfully introduce and avoid confrontations it takes time and effort.
BTW - I have 3 males and one female. I foster cats and kittens all the time and eventually I do intergrate them but very very slowly. At night the newer fosters are put back into their rooms as I cannot supervise.