Welcome to the community and thanks for posting Neil!
The tiles are always laid out left-to-right, top-to-bottom and will automatically reflow as your browser/device width changes (this should be similar to what you experienced in ActionTiles).
As such, the recommended approach is generally to design a dashboard for each device size. If the devices are similar in size (eg. two phones), you might be able to use a custom Tile Size that scales well between two devices that are very close in size (example here)
For tablets that have a similar aspect ratio but different screen sizes, you may be able to use the scaling feature native to your browser. For example, in Fully Kiosk Browser (which is commonly used on Fire Tablets), you can use the ‘Initial Scale’ setting to scale things up and down to reuse a dashboard with the same ratio - there are trade-offs with this approach though.