Made a transmission crossmember for my car, hope this will work. Its 1 1/2" thick wall, and it slides into the 2" thickwall nice. Plan is to weld the two ends in the car, then slide one end of the crossmember in one and drop it in the other, and it will be drilled and bolted. Will make a rubber pad for the mount in th middle. Hope it works.
Just make sure you have the clearance from the floor of your vehicle to allow you to lift the one end of the crossmember up and out. You could mount the bracket the crossmember drops into so the crossmember enters from the front or the back and not the top if you have clearance issues with the floor. Also keep in mind that when you lift the crossmember in order to remove it, you will have a trans attached (or above it, supported by a jack stand), so you need to make sure that with the trans pushed up against the floor you still have room to lift the one end of the crossmember. Have you given this a dry run? I know you can slide the small end into the larger bracket (straight on), but are you sure it will allow you to lift the other end when the brackets are welded into position. If the tubes are a tight fit you might have some problems here, and if the tubes are loose enough to allow the lifting, are they so loose that you might get some clunking when driving the car? By a "dry run" I am suggesting that you mount the brackets solidly to something (even your frame rails) and make sure that it functions the way you expect it too. I can't help but wonder if it isn't able to lift, similar to an antenna, they slide in and out but you can't angle one and not the other.