Can a standard accessory view be in a different position within a UITableViewCell?

No, you cannot move where the accessory view is. As an alternative you can add a subview like the following;

[cell.contentView addSubview:aView];

Also, by setting the accessoryView property equal to something, the accessoryType value is ignored.

There is a way to move default accessoryView, but it's pretty hacky. So it might stop working one day when a new SDK arrives.

Use at your own risk (this code snippet moves any accessoryView 8 pixels to the left. Call [self positionAccessoryView]; from inside the -(void)layoutSubviews method of the desired UITableViewCell subclass):

- (void)layoutSubviews {
    [super layoutSubviews];
    [self positionAccessoryView];
}

- (void)positionAccessoryView {
    UIView *accessory = nil;
    if (self.accessoryView) {
        accessory = self.accessoryView;
    } else if (self.accessoryType != UITableViewCellAccessoryNone) {
        for (UIView *subview in self.subviews) {
            if (subview != self.textLabel &&
                subview != self.detailTextLabel &&
                subview != self.backgroundView &&
                subview != self.contentView &&
                subview != self.selectedBackgroundView &&
                subview != self.imageView &&
                [subview isKindOfClass:[UIButton class]]) {
                accessory = subview;
                break;
            }
        }
    }

    CGRect r = accessory.frame;
    r.origin.x -= 8;
    accessory.frame = r;
}

I was able to change the accessory view's frame by simply doing this in my custom cell subclass.

CGRect adjustedFrame = self.accessoryView.frame;
adjustedFrame.origin.x += 10.0f;
self.accessoryView.frame = adjustedFrame;