要解决API网关无法将大型负载发送到SNS主题的问题，可以尝试以下解决方法。

1. 使用SNS批量发布API：如果负载过大，可以将负载拆分成多个消息，然后使用SNS的批量发布功能将这些消息一次性发送到SNS主题。以下是使用AWS SDK for Java进行批量发布的示例代码：

import com.amazonaws.services.sns.AmazonSNS;
import com.amazonaws.services.sns.AmazonSNSClientBuilder;
import com.amazonaws.services.sns.model.PublishRequest;
import com.amazonaws.services.sns.model.PublishResult;

public class SNSPublisher {
    public static void main(String[] args) {
        AmazonSNS snsClient = AmazonSNSClientBuilder.defaultClient();

        String topicArn = "your-topic-arn";
        String payload = "your-payload";

        // Max number of messages per Publish request is 10
        int batchSize = 10;

        // Split the payload into multiple messages
        String[] messages = payload.split(" ");

        // Publish each message in batches
        for (int i = 0; i < messages.length; i += batchSize) {
            int endIndex = Math.min(i + batchSize, messages.length);
            String[] batch = Arrays.copyOfRange(messages, i, endIndex);

            PublishRequest request = new PublishRequest(topicArn, String.join(" ", batch));
            PublishResult result = snsClient.publish(request);

            System.out.println("Published batch: " + result.getMessageId());
        }
    }
}

2. 使用异步发送：将发送请求变为异步操作，以便API网关能够处理大量的负载。以下是使用AWS SDK for Java进行异步发送的示例代码：

import com.amazonaws.services.sns.AmazonSNS;
import com.amazonaws.services.sns.AmazonSNSAsync;
import com.amazonaws.services.sns.AmazonSNSAsyncClientBuilder;
import com.amazonaws.services.sns.model.PublishRequest;
import com.amazonaws.services.sns.model.PublishResult;

import java.util.concurrent.Future;

public class SNSAsyncPublisher {
    public static void main(String[] args) {
        AmazonSNSAsync snsAsyncClient = AmazonSNSAsyncClientBuilder.defaultClient();

        String topicArn = "your-topic-arn";
        String payload = "your-payload";

        PublishRequest request = new PublishRequest(topicArn, payload);

        // Send the request asynchronously
        Future futureResult = snsAsyncClient.publishAsync(request);

        // Do other processing while waiting for the result

        try {
            // Get the result when ready
            PublishResult result = futureResult.get();
            System.out.println("Published message: " + result.getMessageId());
        } catch (Exception e) {
            // Handle any exceptions
            e.printStackTrace();
        }
    }
}

通过以上两种解决方法，您应该能够将大型负载发送到SNS主题并解决API网关无法处理大负载的问题。