I dont see the advantage to pulling air from a floor vent, Its the same air thats in the room already. It would be a lot easier to just open an inlet vent in the tent near the floor. You will get the same exact air for a lot less work
Pulling air from under the house on the other hand would be a good idea if you didnt have AC. The air under the house will be cooler in summer. You have AC, so no need to go to that trouble.
I run two separate fan systems in my grow tent.
The first one pulls air from outside via a nearby window. The duct is just stuck in the bottom of the window so it sucks air from outside. That air is pulled through the tent and blown into the room through a DIY carbon filter. I have an STC1000 temp controller that turns that fan on/off depending on the tent temp. If it gets too hot, the fan turns on. When the temps drop, the fan goes off. Basically the fan is on almost full time when lights are on, and its off most of the lights out period - unless its hot - I have no AC. So this fan is for temp control, fresh air, and smell reduction - all automatically controlled from a $15 controller.
That same controller also turns on a small heater when needed durring lights OFF if the tems drop below my settings.
The second fan recirculates air within the tent. It pulls air out of the top of the tent and runs it through another DIY carbon filter, then blows it back in the at the bottom of the tent under the canopy. This fan runs 24/7. It is also for smell control and also circulates air below and through the canopy and mixes the air in the entire tent.
Im just using two cheapo bath fans from HomeDepot. They are a little noisy when both are running. If I wasnt so cheap, it could have been a lot quieter