How can I raise a CMOS 1.8V output to 5V LVTTL input with a MOSFET?
The NTE2987 device does not seem to be at all appropriate.  Its VGS threshold is not guaranteed to be low enough and also since it is a large power device its capacitance will be very large.  I expect it is the capacitance feeding through the input signal that is giving the unusual signal on your scope trace.

The VGS threshold shown on data sheets is the voltage at which the device passes a few hundred microamps - it is not fully turned on.

Since you are driving it with a 1.8v logic signal you need a device with a typical threshold voltage of around 1v or so.

I have normally used a device such as a BSS138 (Datasheet) in this type of circuit.