Here's the underside after the wheels have been screwed into the "axle housing". This is simply two pieces of wood sandwiched, 8 inches long, attached to the bottom of the cart to the sidepieces/handles. This was placed in relation to how the cart would balance when the wheels were installed. The cart should be heavier in back, so keep the wheels forward. Drill between the two pieces of wood and use a wood screw and 2 washers (on each side of the wheel) to attach.
Notice again the joints in green, and the newly installed rear supports and their bracing in orange circle . The braces are easily done with a 45 degree angle at each end of a piece of scrap. The supports are 5 inches long, giving the cart a wee pitch to the rear.
As an afterthought, I decided to add some siderails. .75 inch wide pieces cut to fit the front  cross-wise first (1), then two side pieces to fit the remaining length of the deck.
Next, drill out holes to correspond to your choice of uprights. Use a hole smaller than the upright and carve/grind the ends to fit inside (remember, a square peg fits a round hole much tighter). Do both ends of the uprights, and attach a toprail in the same manner.

Important note; I did a little trick to strengthen the rail. Notice that the cross section in front is the one with the holes for the uprights. When attaching the toprail, I   connected it to the corner uprights. This way, two directions are being reinforced, resulting in a sturdier arrangement.
Here's our old-dude refugee, waiting for the old-lady to get ready so they can beat it out of town. She's probably doing her hair.
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