"I have had problems in the past when switching from one vendor to another ..."

This is the price you pay for using a digital device in an analogue function. The same applies (with a vengeance!) to such well known bug-bears as MMV's, analogue switches (4066, 4051, etc.) and PLL's; a Philips 74HC(T)4046 is definitely not the same as one from Fairchild.

"Most probably the input impedance of the 74HCT04 is slightly different from 7404 or 74LS04." (my emphasis)

Yerwhat? There is a huge difference between the input of CMOS (HCT) and bipolar devices (LS). The CMOS input is essentially a capacitor of about 5-10pF while the bipolar device looks like a diode in series with a resistor to Vcc.

A good reference on the subject of crystal oscillators using logic devices is Fairchild's AN-340

Best regards,
Rob.