The “monolithic” option you outlined above exists - typically in larger commercial/industrial operations. Your biggest issue will be controls. Outside of that the efficiency in that arrangement really depends on material used.
The simplest approach would be to use a plate type core that your EA and OA pass through (but do not mix). This is your standard heat recovery arrangement.
I don’t follow the coil arrangement you outline - seems along the line of a glycol loop or heat pipe, which has been proven to be the least efficient method of recovery (45% max under optional design and condition). They still use them but not very often.
If it were me (and it ain’t! 
) - I would look to see if you can buy a standalone plate type core (they exist, just depends where you are from) and duct in and out of one of them. Easy peasy.