I'm fairly out of my depth here. If I could see it, I might be able to identify it, but I'm also working with an ecosystem I'm not personally familiar with.
To summarise for the squeamish - I'm wondering if these things are insect larvae, hatchlings, possibly feeding off something on the other side of the ceiling above the kitchen bench. Detailed discussion follows, if this sort of thing really bugs you (ha ha) don't read on. But to fully understand - sorry for the detail. Warning for the squeamish among you - this could get gruesome.
Kjs, from your description it DOES sound like an insect nymph, probably hatchling, of some sort. Generally ticks and mites closely resemble the adult, even as hatchlings. The only difference between the hatchlings and the adults in these non-spider arachnids are that they often only have 6 legs, not 8. They get the extra paid of legs generally on the first mount. They'll go through several moults before the adult stage is reached.
So, the 'ridged' description you give, plus 'not round' leads me to think it's an insect nymph os some sort. You were quite definite that it's not American cockroach nymph - they were much larger in the photo, though, with no scale given. A freshly hatched American cockroach can be as small as 2 mm but wouldn't be less. They also look a bit like they have a slight bend in the middle, which makes them look a bit like they're stretching up to look at things, like an inquisitive puppy.
But you're sure it's not that. The American cockroach is quite big as an adult - several inches long - and there are many other species which are a lot smaller. The German, for example. We get both - not impressed. The American ones are easier to get rid of, you really need nukes to shift the Germans.
If there's no way it's fallen from the ceiling it's still possibly a cockroach nymph, but a much smaller species. But there are other possibilities...
I doubt very much it's flea, tick or louse.
I'm told that flea nymphs look very much like the adults, so the ridged appearance doesn't fit. With ticks, fleas and lice, we can get misled and expect the bloodspots or darker colouring but if they've not yet had a blood meal, they won't have any blood spots, of course. But without a blood meal, they look paler, almost white - which doesn't fit your description.
Another not very pleasant thought - they keep reappearing in the middle of your bench so soon after you've wiped it, with no apparent trace of a trail - could they be dropping from the ceiling? Is there the possibility you have something dead on the other side of the ceiling, and it's dropping bits? We had a dead rat in a crawlway in our ceiling, right where we couldn't get to it, up against the bedroom wall. (You know how they eat the poison and 'crawl away to die'? Well this one crawled right where we couldn't do a darn thing). And the good old Aussie blowfly COULD reach it.
We had maggots dropping onto our bed, through the join where the ceiling meets the wall. And all we could do was wait until they'd finished their job. If we'd sprayed them, they wouldn't have finished their meal and once the poison blew away, more maggots would move in. So we moved out until they'd finished their meal. We let them get on with it, to get it over and done with sooner.
I can cope with most insects but I really do not like maggots.
So - is there something breeding a different kind of larvae (not maggot) on the other side of your ceiling, above the kitchen bench?
If there is, chances are it's not carrying any nasty diseases. It's just the gross-out factor. And hitting just about anything with bleach will kill it. So will hitting them with a shoe. The smell of bleach won't prevent it, especially if they're simply dropping. They may have no choice about it (gravity...)
Can you take a digital photo of the bugs? Then take the photo to a pest exterminator and see if they can identify it. There are a number of very small insects which are actually used by museum curators to clean up old bones.
I really have no idea where you are compared to Texas, but chances are you should have the same or similar insects in your area, I don't think there are many migratory barriers in the US, other than climate.
It could be this particular beastie, or it could be something that looks quite different but does the same sort of job.
There are other similar beetle larvae which aren't after carrion, they'll eat grain, or paper. You may have a box of papers up in the ceiling which are slowly being munched to nothing.
If they're insects (which I suspect) you can get rid of them with pyrethrin-type sprays. Don't bother spraying the bench - it's not the source, it's just where they're ending up. The 'trail' is only of use when dealing with social insects such as ants or termites. It's unlikely to be a termite - they're white, not dark and can't stand the light. They're also bigger.
I'd be checking upstairs. If you have another floor to the house up there, I'm betting it's difficult child's room? Try and pinpoint EXACTLY what's directly above the kitchen bench where these things are turning up, see if there's a corresponding box or container, or something unpleasant (such as a six-week-old forgotten burger) in the area. Remove whatever the source is, then spray it and the surrounding area.
Good luck. Here's hoping you can find the problem. But I doubt this is a health problem, apart from telling you there could be a health hazard somewhere upstairs.
Marg