

What have you done to clean the bed? From the link to the textured sheet, you should be cleaning it between every print - after it cools - with 90% IPA, and if you still have adhesion issues, you should clean it with warm water and a couple drops of dish soap.
Has the TPU been dried? I don’t normally print with TPU but my understanding is that it needs to be lower humidity than PLA; I use dryboxes for PLA and target a humidity of 15% or lower and don’t use them if they raise above 20%. The recommendation I saw for TPU was to dry it for 7 hours at 70 degrees Celsius, to target 10% humidity (or at least under 20%) and to print directly from a drybox. Note that compared to other filaments, TPU can’t recover as well from having absorbed moisture - if the filament has gotten too wet, it’ll become too brittle if you dry it out as much as is needed. At that point you would need to start with a fresh roll, which would ideally go into a dryer and then drybox immediately.
You should be able to set different settings for the initial layer to avoid stringing, i.e., slower speeds and longer retraction distance. It’s a bit more complicated but you can also configure the speed for a specific range of layers to be slower - i.e., setting it to slow down again once you get to the top of the print. For an example of that, see https://forum.prusa3d.com/forum/prusaslicer/bed-flinger-slower-y-movement-as-function-of-z/
What’s the max speed you’re printing at? My understanding is that everything other than travel should all be the same speed at a given layer, and no higher than 25 mm/s. And with a bed slinger I wouldn’t recommend a much higher travel, either.
In addition to a brim, have you tried adding supports?
To be clear, I’m measuring the relative humidity of the air in the drybox at room temp (72 degrees Fahrenheit / 22 degrees Celsius), not of the filament directly. You can use a hygrometer to do this. I mostly use the hygrometer that comes bundled with my dryboxes (I use the PolyDryer and have several extra PolyDryer Boxes, but there are much cheaper options available) but you can buy a hygrometer for a few bucks or get a bluetooth / wifi / connected one for $15-$20 or so.
If you put filament into a sealed box, it’ll generally - depending on the material - end up in equilibrium with the air. So the measurement you get right away will just show the humidity of the room, but if the filament and desiccant are both dry, it’ll drop; if the desiccant is dry and the filament is wet, it’ll still drop, but not as low.
Note also that what counts as “wet” varies by material. For example, from what I’ve read, PLA can absorb up to 1% or so of its mass as moisture, PETG up to 0.2%, Nylon up to 7-8%… silica gel desiccant beads up to 40%. So when I say they’ll be in equilibrium, I’m referring to the percentage of what that material is capable of absorbing. It isn’t a linear relationship as far as I know, but if it were, that would mean that: if the humidity of the air is 10% and the max moisture the material could retain is 1%, then the material is currently retaining 0.1% moisture by mass. If my room’s humidity is kept at 40%, it’ll absorb moisture until it’s at 0.4% moisture by mass.
That said, this doesn’t measure it perfectly, since while most filament materials absorb moisture from the air when the humidity is higher, they don’t release it as easily. Heating it both allows the air to hold more moisture and allows the filament (and desiccant) to release more moisture.