Here's how my commercial cabinet works. The entire floor is expanded metal grate with the four sides of the cabinet underneath that coming together at a point, like an upside down pyramid. At the bottom is a sliding door so you can drain the media into a bucket, usually because you are tring to find a dropped part. The pyramid is sealed, part of the cabinet. The pickup tube is like yours, mounted to the side of the pyramid with the end a few inches off the bottom. The top end just sticks up through the floor. At the top back corner is a small fitting that takes a large shopvac hose. That hose is connected to a SKATBLAST version of a shopvac that sits on top of a small bbl and has a huge canvas filter. The bbl slowly fills up with media, and when full you just dump back into the cabinet. There is also a moisture filter on the airline, the kind used for commercial paint booths. It has what appears to be a toilet paper sized roll of the brown paper towel they use in restrooms. After an hour or so, it is saturated and you change it out, letting the old one dry out. To save your trigger finger, the air valve is a floor mounted pedal, the gun flows air anytime it is supplied. Get the ceramic or carbide nozzles, they wear out quick.
Were I building one, I would try to copy that as much as possible, it works. If you don't make a funnel shaped reservoir under the floor and go with just a drain, I would mount something like a toilet flange under there with a short length of capped off pipe under. That would seal it, yet you could unscrew the cap to drain. Or mount your bucket under there and use it for the supply and return, with a drain valve in the bottom. You want all openings sealed except the exhaust, grit will exit every opening otherwise. I would also keep the media supply internal to the cabinet, the system will clog occasionally and the cure for that is to put a finger over the nozzle and give it a short blast, forcing air back down the pickup tube and clearing the clog. Also blows the media out of the bucket. I would use a cheapie/old shopvac for exhaust, preferably with the exhaust hosed to the outside to keep grit out of your space. Besides saving the grit, the constant vacuum clears the cloud of dust inside and makes it easier to see. A shopvac also has the motor outside the grit stream, something like a bathroom fan the fine grit blowing across the motor will eventually scrub the insulation off the wire coil, ruin the bearings, etc.