Nice job.
About 16-17 years ago I build a bunch of racks using "select" 1x4's for the sides. Like you, I did it to save weight. On a rack that uses boxes as deep as 41 qts it's a really good idea.
A friend of mine needed one that could hold a lot of weight so he had me replace the 1x4's with 2x4's just like you did.
My only word of warning is that after a while in a semi-heated reptile room all of the vertical lumber supports dried out and shrank which caused the boxes to sieze a bit.
How much this will affect you depends on a lot of factors. If the moisture content of your 2x4's was relatively low and your room isn't terribly warm and/or dry you may not have any problem at all.
The good news is that all of the racks were rebuilt and there hasn't been an issue since. All of them still hold reptiles today. But on the occasion I do build a rack like this I use strips of ripped plywood instead of any sort of solid wood. No concerns with changes in dimension that way.
Regarding having a second person which you mentioned later in the video, you can use duct tape to act as a clamp to hold those pieces in place. A long clamp is better but if you don't have one then duct tape does a better job that you'd expect. Believe it or not I learned this tip on a woodworking forum.