'm aware that it's pretty unusual to assume random slopes but fixed intercepts, and that it is not ideal for me to be using SPSS for this task. However, I'm doing this analysis in a teaching context in which I have no other choice.

I attempted to make this happen by leaving Include intercept unchecked but this didn't work - I ended up with a model where the intercepts were all different and the slopes were zero.

In response to Jeremy's comment I took a look at the syntax.

MIXED jobsat WITH physen
/CRITERIA=CIN(95) MXITER(100) MXSTEP(10) SCORING(1) SINGULAR(0.000000000001) HCONVERGE(0, ABSOLUTE) LCONVERGE(0, ABSOLUTE) PCONVERGE(0.000001, ABSOLUTE)
/FIXED=physen | SSTYPE(3)
/METHOD=REML
/PRINT=COVB SOLUTION TESTCOV
/RANDOM=physen | SUBJECT(grpid) COVTYPE(VC)
/SAVE=PRED.

There doesn't seem to be any reference here to the intercept being fixed. I amended the fourth line of syntax so it read

/FIXED=INTERCEPT physen | SSTYPE(3)

but that still produced a model where the intercept was not fixed.