Import records can be used to archive your data. You can set up a script that finds all records that are "completed", archives them to a different table, then deletes them from the first table.
There may be other factors that affect the speed of your layout updates on the iOS devices. You might try simplifying the layout to use fewer conditional formats, unstored calculation fields etc to see if that helps with the slow downs.
The slowdown is caused by sorting. I have to sit and watch a progress bar sorting thousands of records. Takes forever when you need quick answers that are instant on the desktop but sloooooooooow on an i-device.
I will investigate "import records" as suggested.