Run fleet with on demand instance across AZ

Hello,
I wanted to start EC2 fleet with on-demand instances only, and I wanted them to be distributed across availability zones. Unfortunately, I couldn't find a way to do that, and all the instances are always started in a single AZ.
That is not a problem with spot instances, as they spawn in all the AZ.
I was trying to try different allocation strategies and priorities, but nothing helped.
I was trying to do so in AWS-CDK, using both CfnEC2Fleet link as well as CfnSpotFleet link. Bellow is my code.
Is there way how to achieve that, or do I need to use something else?
Thank you.

const spotFleet = new CfnSpotFleet(stack, 'EC2-Fleet', {
    spotFleetRequestConfigData: {
        allocationStrategy: 'lowestPrice',
        targetCapacity: 8,
        iamFleetRole: fleetRole.roleArn,
        spotMaintenanceStrategies: {
            capacityRebalance: {
                replacementStrategy: 'launch-before-terminate',
                terminationDelay: 120,
            }
        },
        onDemandTargetCapacity: 4,
        instancePoolsToUseCount: stack.availabilityZones.length,
        launchTemplateConfigs: [{
            launchTemplateSpecification: {
                launchTemplateId: launchTemplate.launchTemplateId,
                version: launchTemplate.latestVersionNumber,
            },
            overrides: privateSubnets.map(subnet => ({
                availabilityZone: subnet.subnetAvailabilityZone,
                subnetId: subnet.subnetId,
            })),
        }],
    }
});

const ec2Fleet = new CfnEC2Fleet(stack, 'EC2-EcFleet', {
    targetCapacitySpecification: {
        totalTargetCapacity: 6,
        onDemandTargetCapacity: 6,
        defaultTargetCapacityType: 'on-demand',
    },
    replaceUnhealthyInstances: true,
    onDemandOptions: {
        allocationStrategy: 'prioritized',
    },
    launchTemplateConfigs: [{
        launchTemplateSpecification: {
            launchTemplateId: launchTemplate.launchTemplateId,
            version: launchTemplate.latestVersionNumber,
        },
        overrides: privateSubnets.map(subnet => ({
            availabilityZone: subnet.subnetAvailabilityZone,
            subnetId: subnet.subnetId,
        })),
    }]
});

Where launchTemplate is instance of LaunchTemplate and privateSubnets is array of Subnet instances, one for each AZ.