The metal swivel sits quite high and in toward the centre, so there is a limit on the angle. To go to the original hole for the pigtail would be a fairly shallow angle, but if you cut the amount of plastic you drilled through to the minimum you thought would be strong enough to hold the front line load, the front line might consistently be able to feed back through to the correct position.
I wouldn't be confident enough to even suggest someone try it. I still think the Naish Swivel is a better idea.
One thing I did do to help the loop/loop joint between the flagging line (2.5mm dyneema) and the Slingshot bungee to pass through the 6mm tube of the below the bar swivel, was to use the McDonald Brummell splice method on the looped end of the flagging line and splice the loop through the loop on the end of the bungee while I was making the splice on the flagging line. That makes it smaller cross-section than the normal loop/loop connection.
I had to flare the end of the tube slightly as the normal loop/loop could sometimes catch and bunch up then not enter easily.
I have one Slingshot bungee 58cm long and another 64cm long so they seem to be a bit variable in manufactured length.