The fastest way I have found is to export the layout, and open it in a text editor.
<ShellLayoutDataSet xmlns="http://www.epicor.com/Ice/300/BO/ShellLayout/ShellLayout">
<ShellLayout>
<TenantID />
<LayoutID />
<AuthorID>meissnef</AuthorID>
<DateModified>2022-05-17T09:50:31.9075744-07:00</DateModified>
<ShellHomePage><HomePageDataSet xmlns="http://www.epicor.com/Ice/300/BO/ShellLayout/HomePage">
<HomeTileGroup>
<GroupID>26</GroupID>
<Title>Development</Title>
<IsFaveDefault>false</IsFaveDefault>
<Sequence>0</Sequence>
<WebProperties>{"hidden":"false","x":0,"y":0,"width":12,"height":8,"kinetic":true,"sequence":9}</WebProperties>
<Type>L</Type>
<SysRowID>00000000-0000-0000-0000-000000000000</SysRowID>
<RowMod>A</RowMod>
</HomeTileGroup>
Find the HomeTileGroup you want to re-order, and go down to WebProperties. There is a “sequence” parameter than can be changed. Then simply re-import.