Why you posted their eponymous song mystifies me, as it's one of the thrashiest songs they have. The introduction could have easily been a part of the more violent thrash bands, that riff at 2:00 is pure Slayer,
...if Slayer substantially lengthened their typical phrases, altered the basic melodic patterning of the riffs into something altogether weirder, uglier and far more relentlessly chromatic, and offset the rhythms to give you that zombie lurch that so neatly defines much of the sound of death metal. Of all the precursors to American death metal (and maybe death metal, period), Slayer is by far the most influential: it's not exactly surprising that Slayer riffs updated to the (then) death metal state of the art should turn up on a Deicide album.
prior to it they reintroduce the standard thrash beat
There's no such thing as a "thrash beat" or "thrash chug" (the latter referenced below). The mid-paced, palm-muted, staccato riffing style to which you refer has been with us pretty much from the earliest days of heavy metal. It's a technique Deicide deploy in the death metal rather than the speed/thrash fashion: again, longer phrases and the pretty much exclusive use of chromatic movement are the calling cards here.
They lack the weird, constantly shifting quality that I associate thrash-removed death metal with.
Wait, weren't you just trying to compare Deicide to
Time Does Not Heal? You can't have it both ways...
Dead By Dawn starts up promising something on par with Morbid Angel, but those riffs under the verses still have a reliable, standard thrash-chug to them,
No such thing as "thrash-chug": see above.
I wouldn't say that Altars of Madness was entirely removed of thrash influence either, but it was an earlier album and, despite the "extraneous musicality" of some of their keyboard-containing doomish bits, was closer to purifying the genre than Deicide's S/T.
Altars... is a great album, but it's a total mishmash of death metal, speed metal and heavy metal elements all jammed together, and it only works because it's all held together with melodic duct tape and nightmare logic. Besides,
Blessed are the Sick is their masterpiece, and that one's basically
Altars of Madness with a more
Deicide-like approach.