Best way to set up AJAX/JQuery process?

Facing such a problem I would go in a slightly different way. After a record is updated (or added) using a modal dialog I would refresh (using AJAX) the whole table as it is parametrized (page, number of records and pages, filters, sorting). If in the future something changes in the table, it would be easier to be implemented. If the table is long, it is to be shown in pages, so performance is not a sensible problem.

And for making the things easier, for the main table I would use Datatables javascript with server-side processing - it has an API-command for refreshing the whole table content, also it has an automatic way for saving the table state (page, etc.) within browser's memory. Datatables has built-in modal dialog for data entry, but this feature is not for free, as far as I know. But a custom implementation of such a dialog would not be quite difficult.