Lots of rattling and clanking under the car

Ok I have a problem and I hope I can describe it well enough to get some help.
Whenever I am going down the road at a constant speed, the rattling and clanking sounds under the car do not normally occur. However, as soon as I let off the gas pedal there is a CLANK and if I continue to let he car coast in gear it will rattle and clank randomly quite a bit. These noises sound like they are coming from like right under the e-brake/console area. Then, if I step back on the gas there is a clank but then as long as I keep the gas in the rattles do not occur.

If I am coasting down the road in gear with rattles and clanks occuring and I push the clutch in they stop. However, no matter whether it is in gear or not, when I slow down and either drive very slowly or approach a stop there is all kinds of ratteling which I can even feel through the shifter.

Any idea what in the world this could be? U-Joints maybe or does it sound worse? What can I do to start narrowing it down and finding a solution?

Thanks a lot.

Any idea about how to narrow it down?

I put the car on jackstands, put the trans in neutral, and set the e-brake and tried to spin the driveshaft by hand and it seems nice and tight, very little if any movement. I pushed and pulled up and down and side to side down at the rear end of the driveshaft and everything seemed tight. I went to the trans end of the driveshaft and pushed up under the u-joint and it moves up and down probably like half an inch, and moves side to side maybe an eighth of an inch. Is that normal? Then I put the car in gear with jackstands under the axle housing and let it idle in gear so I could get on the ground and watch the driveshaft and listen to it. I could hear the noises but could not tell where they were coming from, but considering I can feel them through the shifter I figure it's from that end. I let it idle in second gear so that it would spin the shaft a little faster and it looked a little wobbly. Is that normal?

This is all of what I have found out so far, and I don't know if it is normal or bad, because I've never done messed with this stuff before.

I should also mention that I just put an 8.8 in the car whereas it originally had a 7.5, and all of this was happening before AND after the rear swap, so I am 99.9% certain it isn't the rear.

Thanks.

Thank you, that's exactly what I needed to know! The driveshaft doesn't move around where it goes into the transmission, but the u-joint moves a lot. I guess I will replace the u-joints and see if that fixes the problem.