AWS SAM CodeDeploy Lambda deployment failure CodeDeployServiceRole AWSLambda request limit exceeded

I have a backend service consisting of 29 Lambda functions deployed with AWS SAM with versioning enabled. In the past few months deployments became flaky and sometimes only succeed after several re-runs, failing with "InternalFailure" error code (visible in CloudFormation, which also now marks it as the root cause of failures). When issues first began, I noticed several "ThrottlingException" errors from CodeDeploy in CloudTrail during deployment, so I experimented with the AWS_MAX_ATTEMPTS and AWS_RETRY_MODE environment variables to allow more retries and also retry smarter; the effects were visible (now the deployment would continue after the default 3 retries), but there were still deployment failures with the same cause. Now I decided to change the CodeDeploy deployment preference from "Linear50PercentEvery1Minute" to "AllAtOnce", hoping it would result in less CodeDeploy calls, which also helped, I no longer see "ThrottlingException" errors in CloudTrail but deployments still fail from time to time. Now, when I check CodeDeploy's deployments, I see the following error message at the time when the CloudFormation deployment fails: The deployment failed because the number of requests by the IAM role arn:aws:iam::[account_id]:role/[stack_name]-CodeDeployServiceRole-[suffix] exceeded the request limit for AWSLambda. Avoid retrying API requests at a high rate. Trying to fix this, I checked the Lambda quotas docs, which says there is a 15 request per second non-increasable quota on Lambda API calls (excluding GetFunction and GetPolicy requests). I checked in CloudTrail, the deployment occasionally goes above 15 calls, mostly by doing GetProvisionedConcurrencyConfig, GetAlias20150331 and UpdateAlias20150331 calls. I'd like to ask if Lambda versioning and CodeDeploy is expected to work with this (and higher) number of Lambda functions, or is this solution only limited to a limited number of functions. If it's supposed to work, how can fix the issue of CodeDeploy's IAM service role getting itself rate limited by calling the AWSLambda API during deployment? As I understand the problematic calls are not done by AWS SAM during deployment, but internally by CodeDeploy, so maybe it can only be resolved by not deploying all of my functions at once, but only a few at a time (or else I need to give up on Lambda versioning)? I checked similar questions, they mention checking the root cause in CloudFormation and the logs in CloudTrail, I've done both, but now it seems to me the issue is clear but there's no simple solution to fix it. Thanks in advance!