And then you search for certain invoice over huge number of rows! (~200 invoicers per day, ~300 workdays in year , ~5 rows per invoice + rows for counts and sums, + 2 empty rows per invoice. And no way to use autofilter.

As I said, you can design a report in any form you want. Probably the best one will be getting a list of all invoices for certain period (date or month or year - with your number of invoices a date will be reasonable choice) with ODBC query from InvoiceData table. The query will be executed automatically whenever period in cell linked to query parameter is changed. The query will return p.e. invoice number and date. You add columns adjacent to query table for every count and sum, and calculate according values using COUNTIFS() and SUMIFS() functions from InvoiceData table.
And you get all needed info in compact (table) form, can use autofilters on report and subtotals on top of report sheet like I used on InvoiceData sheet (I don't have Excel at home, so I can only hope I haven't completly forgotten what name I used for sheet).

Sums and counts under (but better above, as you never know before, how many rows will be in some invoice) an invoice you can have also - when you design a report for single invoice. Again the easiest way is to use query with invoice number as parameter. The query will return full invoice info from InvoiceData table, and you use COUNTIFS() and SUMIFS() to calculate totals from query table.