Coupling caps with the outer foil orientation installed backwards will not cause the hum you are getting. I promise
Now if you had a small amount of floor noise and had use all MF resistors and wanted to get dead quiet maybe then it would be something to try. The problem is stuffing 10 pounds of manure into a 5 pound bag. Something is bound to stink.
I have built a 4 power tube amp in a chassis the size you are using, but I also shielded the power section from the preamp. All 4 power tubes were between the transformers. Choke was inside and 2 cap cans, one for the power side and the other for the preamp. Also, inside the chassis I installed a plate separating the rear of the chassis from the preamp with a hold drilled and a rubber grommet for the signal wires to pass through.
When I installed the chassis cover it essentially isolated all the PA eddy currents from the preamp. I wish I had a photo, but the amp is long gone, but I did have to design my own board for the preamp and the bias board was affixed to the side of the chassis.
I made the same mistake on my second scratch build by wanting to stuff a high gain 2 El34 amp into a 10 x 6 x 2.5 chassis and put all the tubes in a row.
Now when someone ask me about a chassis I will say layout one to fit and then get a one larger.
The main problem is if you do get it quiet a simple tube change in the future could bring it back. Yes, shielded will and can help, but you have already spent most of the money on your parts. You can use the chassis you have for a smaller amp that I am sure you will want.
I have used a 19 x 8 x 2 to build a Marshall Super Lead and put it in a head box 22 wide, but I still put the power tubes towards the back of the chassis and preamp tubes to the front.
Search for a Soldano SLO 100 watter. He uses some nice ideas to layout a shorter chassis, but they are wider.