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I'm just thinking out loud here, but if you a) re-order the data in Mapinfo, and then b) work out a way of perma-saving that reordering in the .tab file, then would that make difference to the order in which results return in SSA?
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I think I have the/a solution for you.
Open the tab file in Mapinfo and run an SQL Query by ordering by the field of your choice (the one that's not in alphabetical order). Save the resulting query as anew .tab. If you then publish that .tab file and view in SSA and click at any location where there are overlapping features the result in left side panel will be in alphabetical order.
I've set up an example at https://geo.southwark.gov.uk/connect/analyst/mobile/#/main?mapcfg=Order%20test.
Turn on the not_in_order layer leaving in_order switched off. Now single click at 532963, 175463 and see how the results are ordered in left side panel: g, y, p, e, j
Now turn on the in_order layer leaving not_in_order switched off. Single click at 532963, 175463 and see how the results are ordered in left side panel: e, g, j, p, y