OK, thanks for the suggestions. I think it is clear a Shop Vac will likely not do the job for the suction side of things.
And to answer Peter, the current location is my deck (uncovered). I roll it on a cart into a little storage room that also houses the water heater. The good news here could be that if I need to mount a hood of some sort above the roaster exhaust, I could use this little room, and even tie into the water heater exhaust if necessary. I also have the option of taking the roaster in the garage, but the garage roof is actually below the first floor, and the water heater room roof is at the 1st floor, so anything coming out of either would have to have almost no smell, otherwise I will get complaints, since it appears to drift into the 2nd story windows downwind.
And I cannot really run any sort of piping or exhaust too high, as I will not only look like a doofus, but also violate about 17 HOA rules while looking like a doofus. Assuming I can get most of the odor out, I was planning on routing the output to a very low level and as far away from the neighbors in question as possible (like out the front of my garage), hoping that it dissipates quicker than if run higher up.
So here is an idea: if I can get an oven hood type setup with enough suction, what type of filtering material would be:
1. The most suitable at removing odor
2a. The cheapest to replace
OR
2b. The easiest to maintain and clean if necessary