Thanks for your thoughts
I wasn’t sure how you were planning to dispose of the eggs especially as some of the over 3,500 species have very resilient eggs:
For instance, Wyeomyia larvae typically get frozen into solid lumps of ice during winter and only complete their development in spring. The eggs of some species of Aedes remain unharmed in diapause if they dry out, and hatch later when they are covered by water.
Also apparently not all species lay their eggs in water – some lay them near water:
Aedes generally drop their eggs singly too, but not as a rule into water. Instead they lay their eggs on damp mud or other surfaces near the water's edge. This commonly is the wall of a cavity such as a hollow stump or a container such as a bucket or discarded vehicle tire. The eggs generally do not hatch until they are flooded, and they may have to withstand considerable desiccation before that happens.
It also seems to be a continual problem in some areas and not just seasonal:
While many species are native to tropical and subtropical regions, some genera such as Aedes have successfully adapted to cooler regions. In the warm and humid tropical regions, they are active the entire year long; however, in temperate regions they hibernate over winter. Eggs from strains in the temperate zones are more tolerant to the cold than ones from warmer regions. They can even tolerate snow and sub-zero temperatures. In addition, adults can survive throughout winter in suitable microhabitats.
Ontop of that they also seems to be able to come from far and wide
Means of dispersal
Over large distances, worldwide introduction of various mosquito species into regions where they are not indigenous has occurred through human agencies, primarily on sea routes, in which the eggs, larvae, and pupae inhabiting water-filled used tires and cut flowers are transported. However, apart from sea transport, mosquitoes have been effectively carried by personal vehicles, delivery trucks, and trains and aircraft. Quarantine measures have proved difficult to apply sufficiently consistently.
I therefore am not sure that trying to encourage breeding, and then putting them on the compost heap may actually result in more mosquitoes as they would likely breed there
(Sorry I tried to post a reply to the last comment but would not work so trying it this way)