I finally captured an Engineer and it just opened up a huge tree of new weapons. Based on this if I had known I would have gone after the early missions more fiercely to get early Engineers as the 1st month or two was much easier than month 6.
My experience was much the same, except it took me to month 13 to clear the bottleneck. The effect, though, has been fantastic, as I've had to rely on conventional weapons for a long time, of which there is an ample selection in FMP, and the few laser/gauss I've been able to collect from missions, saving these for special occasions. After I cleared the initial stages, and found tactics that could avoid major squad wipes most of the time, I only had anthropods/MiB/Hybrids, w/ the odd other race occasionally showing up, and couldn't stun anything of value for a long time. I finally got a sectoid commander in a jungle pyramid, grabbed his body and evac'd, and more recently sectoid and floaters have reappeared in greater numbers, allowing me to finally access engineers and gauss/railguns/lasers.
The gauss/lasers have come all at once mostly though. I might have prefered to need an engineer even to unlock each next one, to draw out the progression further, as suddenly in the span of about a month, my former logistical concerns are all but gone.