Sounds to me like the tyre beads are too high and thus the gap is too big – two layers of yellow tape AND your fabric stuff?!
Stans instructions for 717’s is 1 or two layers of yellow tape only.
Is this a case of RTFM? 😆
Forgot to say, I’d not like to inflate Conti’s with just a track pump, they’re very porous IME.
A compressor is proabably necessary if you want to be able to inflate all brands of tyres, a track pump will usually suffice for maxxis or most genuine UST tyres.