Could be a collapsed drain line, either to or from the septic tank.

You probibly should have it inspected again but here's a few things you can check if it's not arobic.
There should be a clean-out between house and tank,is water standing in it? No, the problem is likly a clogged main drain line,snake it. Low consumption toilets barly put enough water through to carry waste and paper all the way to tank. If and waste and/or paper is lieing in line when you leave for home,it will dry out and catch things on next visit. NEVER flush Kleenx,paper towel,baby wipe,,,,,,let's make this easy and say what you can flush then say absolutly nothing else. Toilet paper and body waste,nothing else. Water standing in clean-out, yes,tanks and absorbsun field are over filled or there is a colapsed distribution box or line. Make sure no facuet or toilet drips. If it's arobic,the pump is probly gone out or power has been lost to the system.

The lowest cleanout between house and tank had cleared the standing water after ~3-4 hours. We snaked all lines, found nothing. We re-ran water in tub and the standing water recollected so it seems like, if there is a physical block, it is close to the tank?

The septic company asserts that it can't be the tank since the last inspection and cleanout were so recent. (Not sure I follow that logic) Maybe I need a new, more curious, septic company.

The rules are only TP and waste but that doesn't mean all guests have respected the rule.

Our toilets are the old high-flow potties so presumably are flushing waste well. There is often the last toilet use before departure, maybe (after we fix this issue) we should have the habit of running some water after the last flush to help ensure the drain pipes ARE clear.

No drippy faucets, no lush weeds suddenly growing...

"Maybe I need a new, more curious, septic company."

On that I believe we can agree. While it's true the tank(s) wouldn't ordinarly require pump out this soon,they should show more intrest in the problem by giving you answers you came here looking for. How long has the system been in service? Is the cloths washer on septic? Do you use bleach? Is the dish w detergent septic friendly? Just for grins do a neter check to eliminate unknown leak that could be filling tank. According to your observations at the clean-out,you can ignore all lines upstream from there until clean-out isn't standing water. Conventional septic systems don't lend themselves to diy troubleshooting and even if they did,less than 1% of homeowners are willing to get that down and dirty. With your above average determination,you may find the problem. It shouldn't be more than 20 feet from house to tank which is easy to snake. How certain are you of how many tanks you have? You can fihd out probing with a steel rod ,preffibly one desighned with tee handle for the purpous. How confident are you they were ALL pumped and inspected? Were you there or did you at least notice how many places were dug up? Do you know how and where the leach field is laid out? The difference in grass between functioning and nonfunctional laterals is not easyly detectable other than after long drought conditions,even then only if system is handling alot of water. When this happens without obivous reason,I normaly suspect a problem with first 6 feet of line where it leaves tank to leach field. The line normaly leaves tank about 2 feet below surface,runs 2 or 3 feet before turning down to 3 or 4 feet below surface and level with leach field or distribution box. It is within these crooks,turns and connectors that ground shift or settleing can have the worst effect by crushing or pulling apart. It's a rag tag method of determining if leach field is failing ( #1 reason for septic problems) but digging that first section up can help reveal a failing field. Additional to the obivous tools,have on hand , 10-32 or larger stainless steel screw,self tapping or with tap,drill motor and proper bit for tapping the screw. A sump pump is desirable just in case it's needed but if there is a rental or retail nearby the pump can be deffered until and if needed. While water is backed up as it was in your discription,drill hole at lowest point you have exposed. No water or only droplets with zero pressure definitivly shows problem is toward house. A stream squirting tells you the problem is downstream. Now use the screw to plug the hole. Tree roots are common. Leach field failures are a whole new kettle of fish so lets don't go there until absolutly nessary. Noone envys you. Good luck