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This is a hard question to answer without knowing the reasons why your site is possibly under performing on page speed tests. There could be a variety of reasons. I'd recommend a caching plugin, and that your images are all appropriately sized and then, as Stramark suggests, you could look at a CDN to help alleviate the problem. A new theme/template may help, but is unlikely to be any sort of silver bullet.

even after correctly redirecting it could take a few days to a few weeks to have your stable position back. So if your business would hurt extra in summer, do not move until after the season. (appart from the risk you are taking if you or your webbuilder does not have the experience to do this correctly)