WordPress : auditing, improving existing site and server set up

Need pro wordpress-er with AWS experience to help out with server-side performance, and also within the wordpress plugins. Target site gets 30k visits a month and growing: Known issues that we need help with : - The theme is too large and chunky and has many plugins or extras that we don't need. - The AWS server doesn't seem to be set up correctly, it's costing us more than it should and it doesn't handle large traffic very well - Site seems slow when there's a few people on it - Very slow if there's a few editors in the back end - The cache doesn't work very well, if we change something on the site, for example the author of a post, it doesn't show up to readers for a few hours, so we can't make quick fixes - Mailboxes seem to work sometimes but then stop working other times - We get 504 errors and the site falls off from time to time - Picture uploader in the media library very often doesn't work, takes 3, 4, 5 or more attempts sometimes (Paddy will tell you) - Search function doesn't work too well, can't search author names, for example This work will be an initial audit, followed by continues maintenance of the site on a monthly basis.