WHM - cPanel Expert Needed - Transfer Hosting To New Server

We currently have a managed dedicated server with UK Fast and we need to upgrade to a new server. All the websites are WordPress and we have around 90 accounts, many of the accounts have multiple domains/websites.

We currently have 63 of the website associated with the hosting routed directly through our Cloudflare account. The others we would need to seek access to.

We are looking for someone who is very experienced with transferring accounts from one server to the next with minimal disruption to the website and emails.

We will have 1 month where we do not need to pay for the new server and then an additional month where we only have to pay for the software. So this doesn't need to be done in a huge rush.

Please let me know of your experience and detail how this can be carried out and what the implications will be.

PLEASE DO NOT CALL