i think one inline fan may suffice for the 2x1000w lights, the way i would duct them if trying to dump the heat into your house through the registers would be
Intake-->pre-filter-->dump low into grow. the intake should be equal to 3x the exhaust size or your just going to be making your fan struggle. So an 8" exhaust would be around 25 cubic inches of space. so you would want something with 75 cubic inches of space equivalent for passive intake.
now the pre filter should also be increased because its going to form a restriction, so it can be good to just really oversize the thing and put a cheap rewashable cut to fit filter in there instead of a pleated.
after the intake comes into the room low, you could hang your carbon filter high with the lights-->pipe through both lights--> to the exhaust fan, then exhaust down into the duct or something .
this will make the cool air come in low near the roots and then all the heat will draw out of the high part of your room keeping the foliage at a median temperature.
I dont see any oscillating fans in there but its important to have a few for a room that size especially, you want your plants to wiggle a little bit and not too much. Too much airflow causes over transpiration and causes the plants to try to maintain moisture in the leaves more than focusing on growing, but too little air flow the plant wont beef up from being wiggled around .
personally, i dont like using the glass on the lights, you can duct them together and have the glass off and it will put out much more light because the glass acts like a filter
it is good to prefilter your room so dust doesnt collect on your plants leaves and on your lights and walls
a great way to see if your room fans arent getting enough intake.. i see you have a door there. once everythings hooked up, you should be able to tell if the intake is big enough for the exhaust if the door flys open when you open your room, or slams shut depending which way it opens
the problem with building your veg room inside your flower room is you will only be able to access and work on the vegged plants when the flowering chamber is on because the light when you open it will wake them up..
if you have no way around building it inside ur flowering room, try adding an additional switch on the outside of your veg room to shut all the lights off, and add a few green lights that you can use while everythings asleep. i bought the illuminati bulb it was expensive but is a pure green led bulb instead of one of those cheap painted CFL bulbs that i dont trust.
u can also get a green LED headlamp
i keep adding so heres one more important thing about fans.
you want to minimize bends, and if you have bends, u want to ideally have them 5' away from either end of your fan to maximize velocity. youd be suprised with the proper intake and fan setup how low the fan speed can run and still keep the heat down
FURTHERMORE.. lol
to utilize one fan only, for both chambers, will restrict airflow but is possible. 875 cfm is a lot.. those puppys must be loud AF.
you could go intake-->drop low into veg---> have a hole at top of veg that has a pipe that goes back down (lighttrap)---> open to floor
then up high carbon filter to lights to the fan then down to the register. id choose a return register so your not fighting your heating system