* Consider using op amps which may have a built-in slew rate (perhaps user adjustable). The slew rate creates a delay effect.
Configure to invert signal. Or schmitt triggers might do the job.
(Example, in Falstad's 741 op amp, there is a single capacitor in the internals. Increasing the cap value lengthens transition time.)
* When I use invert-gates simulating sequencers (chasers, ring counters), I find it improves reliability to put the RC delay at every gate's input. Otherwise it's hard to prevent the circuit from lapsing into unwanted two-state oscillation mode.
* Sometimes I must add an extra invert-gate (two gates in a row) in order to have the proper number of polarity inversions.
* Sometimes it helps to apply 1/2 supply V through a high-ohm resistor to each input. (Reason: 1/2 supply V is the threshold around which invert-gates change state.)
* Also try grounding the first input as you power up. Admit several preliminary clock pulses until the entire ring of devices is set to the same state. Then connect the first input to the final output. If you're lucky you get desired behavior (that is, one and only one change of state rotating through the devices).