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@Oswald
The way I see it the biggest problem you currently have it the shifter and cassette incompatibility .. The centre to centre spacing of each cog on the cassette is 4.8mm. The shifter should pull cable to make the rear mech move 4.34mm. So assuming you've set the rear mech to perfect alignment at the top of the cassette by the time you've shifter to gear number 8 the rear mech is 4mm approximate in the wrong position. The only way around this with the current set up is friction shift, which you're opposed too, change the cassette to 9 speed .. or a complete new drive train. That's my 2p .. Although there could be some parallelogram incompatibility with the rear mech translating the cable pull exactly in the mech due to design or wear .. And 3/32 is the roller width or internal chain width so as long as the DA ring is 3/32 it will fit. The difference between 9, 10 and 11 chains is the outside width which is important on a derailleur system to ensure the chain doesn't rub on the next cog on the cassette. You will need a derailleur chain though, not a track chain, because these have a 'flexibility' to 'bend' slightly as the chain line moves to less ideal at the extremes of the cassette