Afaik the HC14 hysteresis is 0.9V thus much more than the amplitude OP is feeding in.
I measured it to just over 0.5V on a couple of different TI 74HC14's I have (DIP), with a 3.3V supply. This is why it's important to know what the logic voltage is, because the hysteresis depends on the supply voltage. I never got an answer to that.
Unless the cable is ridiculously long or the source does load detection, there's zero benefit in terminating a 275 kHz signal into a 50ohm load. It's just a pure voltage signal. Power is irrelevant. Use a shielded cable and terminate it into e.g. 22k. This will produce a stronger signal.
Admitting that hysteresis is important,
which in fact is, you should use a comparator for your first stage. It is a bad idea do use logic directly for that, especially when dealing with signals that only have 600mVpp of amplitude. It is not guaranteed that you'll always get a decent signal out, and if you do, it may as well not having a 50% duty cycle. The hysteresis of a Schmitt trigger is not finely tuned and will depend on many factors, and not just supply. To aggravate, the output signal will be out of sync.
You are much better off using a comparator, since that you can even adjust the amount of hysteresis you wish. Plus, there are very fast comparators on the market.
For example, this is what I got with the schematic shown in my post above. Notice that the analog signal you see is an amplified version (2.43x) of the signal going to the comparator. The digital signal is generated by the comparator, but going through a clock buffer before the output. Both outputs were terminated. See the image attached. The schematic may help, but is there just for reference.
Kind regards, Samuel Lourenço