CLOSED - borrowed a micro-rooter & dealt with the problem myself. Thanks for your interest.
My problem area is isolated to the basement drain line somewhere below the Y-connection of the basement utility/laundry sink & kitchen drain (coming from upstairs) and the connection to the main drain line. Itâ€™s approx. 4-5 feet of line running below the concrete but you can access it from either the plug at the Y where the two drains (utility & kitchen) connect or from the main drain.
I've been in this house for 2 months and it was sluggish from the get-got but, now it's totally blocked. Very likely the addition of silt & dirt (waste-water from cleaning the basement flr), saw-dust (kitchen renos), etc didn't help & now it's totally blocked (the kitchen sink drainage backs up into the utility sink). I've tried baking soda, vinegar, salt, hot water, drano, plunger, little hand snake (it was a pretty crappy one), repeat, etc to no avail. (thankfully, I have access to the main drain & that's not blocked)
I'm sure it would be a cinch with the right tools (ie, big wrench to open the pipe cap & heavy-duty auger/rooter) but, I don't have them.
I'd like this fixed asap (on a budget that would cost less than a profesh plumber) & would prefer not to miss work if possible (so early morning, evenings or weekend would be great).