Direct Outs from the Mackie into the 1010 inputs set at +4....but those sneaky direct outs are not so direct, they are POST Eq & Fader, sooo the CLEANEST signal would be from the insert jacks. But they're unbalanced. And so am I. Try both and listen. The (in)direct outs can accept a balanced TRS cable as can the 1010. Not sure if the 1604 insert jack output is -10 or +4. Ask a Mackie expert, I'm just a mandolin player with an audio obession. I use outboard pre's into my 1010. But have used the insert jack from the Mackie on some live gigs. The plug should only be pressed into the first 'click' position with a normal 1/4" cable. If you insert it all the way, you get stunning silence as there is no return.
Connect your 1010 outputs to the 1604 inputs using balanced TRS cables... just not the same channels that are connected to your 1010 input channels. Set the 1010 outputs to the +4 position. And as you probably know, you will need to mess around with the Delta control panel to setup monitoring as required.
I would never suggest using any of the sub-mix or main mix outputs as the Mackie summing buses are sort of sucky. As in sucking the life force from the signal. But if you need 16 live tracks into the 1010's 8 inputs, then you gotta do what you gotta do.
And as with all things Mackie, watch your gain stages. Closely. Very closely. Once your magical musical signals have entered the cramped quarters of the 1604 polite discretion is required at each stage so the agitated electrons don't rebel in their opamp hell and cause an auditory grungefest. Mackie claims +15 dB headroom, but that's in 'dog' dB's so you need to divide by 7!
Hope this helps,
Jim