This year some of my Gurney's Whopper strawberries, a June-bearing variety, produced a few berries in the fall. That might weaken the plants for next years crop. Will culling them for this be effective or do they do this randomly ?
I am attempting to answer this because someone better qualified has not...
I don't have much experience of the north hemisphere growing season but I do know that in the Adelaide Hills near where I live (roughly Meditteranean but cooler at this higher altitude) huge crops of strawberries are produced from now until the end of April which corresponds to mid-spring to mid-autumn (mid-fall). This is on an industrial scale though, so industrial scale watering and nutrients are going into them. Still, I don't know that late strawberries would necessarily weaken your plant. I'd say it just means you get more strawberries than everybody else.
Something I found that might help is advice from an Illinois university information page on strawberries. It suggests that removing all flowers in the first growing season will encourage the roots and runners to develop and thus give you a better crop thereafter. This implies that removing flowers at a time when they are taking the lion's share of resources will strengthen other aspects of the plant, which makes sense. It goes on to specifically say that you should let the fall/autumn flowers remain:
For everbearing and day-neutral strawberries, remove the flowers until the end of June and then after that date allow the flowers to remain to set fruit for a summer/fall harvest.
My feeling (merely opinion of course) is that removing late fruit (which presumably is just a smattering), wouldn't help that much because plenty of resources are still getting through to the rest of the plant.