Reusing module with aws_apigatewayv2_api - terraform-provider-aws

Question

I have a module with a lambda and an API gateway that integrates with it. At a high level, it basically looks something like this (intentionally omitting a lot of detail):
resource "aws_lambda_function" "my_lambda" {
function_name = var.v1 ? "v1_lambda" : "v2_lambda"
handler = var.v1 ? "myV1Handler" : "myV2Handler"
}
resource "aws_apigatewayv2_api" "my_gateway" {
name = "my_gateway"
}
resource "aws_apigatewayv2_route" "my_gateway_route" {
api_id = aws_apigatewayv2_api.my_gateway.id
route_key = var.v1 ? "GET /v1/..." : "GET /v2/..."
}
resource "aws_apigatewayv2_integration" "my_gateway_integration" {
integration_uri = aws_lambda_function.my_lambda.invoke_arn
}
What I'm trying to do, effectively, is set up 2 lambdas that differ only by handler, with a single API gateway basically hosting both functions on different URLs (hence the /v1 and /v2). My thought was I could achieve that by reusing this module at the root, like so:
module "v1" {
source = "my_module/"
v1 = true
}
module "v2" {
source = "my_module/"
v1 = false
}
Unfortunately, this does not work, as Terraform attempts to create a duplicate resource and fails. What is the best practice to achieving my desired outcome?