I am not sure how a predator top heavy ecology could be conceived as an hourglass unless the predators at some trophic level were underutilizing the pray for some reason. Or is that a presumption of predator overutilization? The box graph assumption gives me the impression that each food chain level is strictly stratified with each level working at perfect efficiency. This box graph is perhaps related to a quote in the paper fundulus mentioned:
"Trophic Structure and Productivity of a Windward Coral Reef Community on Eniwetok Atoll" by Howard T. Odum and Eugene P. Odum, 1955, an Ecological Monograph of the Ecological Society of America.
It has long been felt that the productivity of the various trophic levels of a community is very roughly proportional to the standing crop being maintained although the reason has not been entirely clear.
Consider a highly simplified system for conceptual purposes. You have an autotroph such as an algae with a predator that feeds on it. The predator overgrazes the alga to the point they limit their own food supply and goes through starvation cycles. Only a very small percentage of the predator population is needed to maintain a healthy population level. Meanwhile, during the starvation cycles of the predators the algae is overgrazed. Hence the abiotic resources used by the algae go underutilized for lack algae to utilize it. Think of the massive nutrient load we are choking rivers and estuaries with, in which the major limiting factor is abiotic, i.e., the oxygen it depletes from the water.
Now if we add a second predator B that feeds on the first predators A what happens? Then B can feed on the majority of A without effecting the ability of A to maintain a healthy population. Also removing the least fit among A making what population remains healthier. Also reducing the overgrazing on the algae, reducing underutilization of abiotic resources consumed by algae, so that ideal population levels of predators A is greater with B than without. Now potentially B can over predate on A, resulting in underutilization of algae such that both A and B experience periods of suppressed population levels. A third predator of B would stabilize it even further. In some cases to some degree the same effect can even be provided by predation of the young of the same species.
This overly simplified food web optimizes biomass production but does not explain the top heavy distribution predators in living biomass. Consider the bottom producers, algae in this case. Algae reproduces some number of times and eventually dies. But with predators present some chance exist that it ptoduces some number of times and is then eaten. So what would have otherwise been dead biomass is now swimming around looking for its next meal. This continues up through all trophic levels, where even those that die of old age becomes food for predators on their carcass. Hence the increase of biomass among the top predators is not the result of removing that biomass from their prey (where I presume the hourglass comes from), but by increasing the total volume of biomass that remains living at any given time. You also have different lifespans, metabolic rates, etc., to contend with. Consider our own consumption rates if we required the same consumption relative to body mass as a shrew. The body mass of a predator is often determined more by successful survival than it is consumption rate.
The model described is massively oversimplified. Intended only to illustrate that the biomass available to living organisms is not limited by the biomass of available prey. The available biomass actually grows continually as a product of autotrophs which in turn depend on predators. Most fundamentally in the carbon cycle but in many other ways as well. The feedback between trophic cascades and resource limits increases the overall efficiency regardless of the efficiency of any one variable.
With respect to snakeheads and introduced species we simply do not know in any given instance what species we are relieving pressure on or adding pressure to. Due to the effects described just because a snakehead predates on a given species does not mean any overall survival pressure has increased on that species, perhaps even reduced. Likewise, the fact that a species is not being predated on is no indication that their survival pressure is not increased or decreased. It is a crap shoot. We simply do not know. It does not take pushing a species over the edge for these survival pressures to incrementally increase or decrease either directly or indirectly.