Limiting Current interference in Photomultiplier Amplifier Circuit
Glad to see somebody else is using silicon photomultipliers! They are nifty devices, I've been playing with them recently on a project.

First off, I'm not seeing a bias across the device - remember, you have to bias the silicon photomultiplier past its avalanche breakdown point to get any avalanching in response to photons. While the SPICE model may give you a current pulse when you trigger the fire input, this is not the real behaviour of the device. In your case, the grounded cathode should instead be raised up to about 27.5V to bias the SensL device into operation.

Unless cost is a significant issue, I would use four transimpedance amplifiers to read them out, one for each channel. This will solve your backfeed problem. Something like the OPA4354 (4 amplifiers, 250MHz GBWP, $8 in singles) might work for you. Since the SiPMs themselves are quite a bit more expensive than this, it probably won't break the budget. If you need to add the channels together in analog, this can easily be done afterwards with a resistive summer.

Keep in mind that if you read out at the anode with a transimpedance amplifier, the signal from your transimpedance amplifier will be inverted. This isn't an issue if you have bipolar supplies or use a virtual ground, but I thought I should mention it. If I recall correctly, anode readouts from the SensL devices are preferred for speed since the cathode is tied to the package ground and has greater capacitance.

Noise should not be a problem with a SiPM setup, since the current pulses are discrete (1 pulse height = 1 photon) and the peaks are well above the noise floor in a properly designed circuit. I would skip the feedback capacitor in the opamp circuit altogether unless you're having ringing problems. As you have likely surmised, adding the feedback capacitor in parallel with the feedback resistor creates a lowpass filter, which is going to directly impact your rise time. So, only do this if you need to combat ringing.

Finally, if you need extremely sharp risetimes, I would look at using the capacitively coupled fast output of the SensL device instead. This is described in the C-series manual.