Website Transfer to new Workspace plan

Hey there. We first created our company website on the Webflow account of one of our employees on the CMS plan. Once we realised that more people needed to work on the site we created a new workspace with the Growth plan. Therefore we followed Webflow iinstructions, and tried transferring the site during a downtime while activating the new plan. Unfortunally the transfer did not work. Now we have two plans that we pay for but the site is still in the limited CMS plan account and not the shared space it is supposed to be in.
Does anyone know how we can transfer the site to the other plan without experiencing another downtime?
Thanks in advance