how to make curl uploads faster with firewall
Solution 1:
Generally firewalls will either stop connections or allow them - not slow them down.
In the absence of a lot more information about what's going on here, it's impossible to make an even an educated guess as to what's happening - if you don't know how to start investigating the problem then go speak to the people whom you are paying to provide support for the service.
One of the many things you've not mentioned is where the firewall is - if it is at your end, then provide some info about how it is configured. If it is at the remote end, then you won't have access to the config and won't be able to change it - again, speak to the people supporting it.
You've also not provided any information about the location of the old and new server relative to where you're uploading data from nor the configuration of your internet connection.
Nor have you provided any info about how the problem varies by file size (a consistent delay for all operations regardless of size would suggest a DNS issue, a delay increasing with file size would indicate a latency / bandwidth / window scaling issue)