Multi-agent large language model (LLM) systems increasingly combine model-generated judgments for forecasting and collective decision-making. However, homogeneous agent systems, i.e., those that share a model and evidence, may produce correlated forecasts, and communication may further contract the diversity that remains. We examine these issues in live LLM prediction polls. Across 189 resolved snapshots, mean residual-error correlation was 0.910. Semantic prompt differences were associated with forecast differences, but diversity-aware selection did not detectably outperform prespecified random ensembles. Standard deliberation removed approximately twice as much disagreement benefit as it added through improvements in individual forecasts at the point estimates, with no detectable improvement in aggregate accuracy. In a prospective intervention, a probability-blind summary of forecast-relevant claims retained 93% of initial dispersion, compared with 29% under standard exchange.