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?
Wow, there isn’t a single solution in here with the obvious answer?
You’ll need a domain name. It doesn’t need to be paid - you can use DuckDNS. Note that whoever hosts your DNS needs to support dynamic DNS. I use Cloudflare for this for free (not their other services) even though I bought my domains from Namecheap.
Then, you can either set up Let’s Encrypt on device and have it generate certs in a location Jellyfin knows about (not sure what this entails exactly, as I don’t use this approach) or you can do what I do:
On your router, forward port 443 to the outbound secure port from your PI (which for simplicity’s sake should also be port 443). You likely also need to forward port 80 in order to verify Let’s Encrypt.
If you want to use Jellyfin while on your network and your router doesn’t support NAT loopback requests, then you can use the server’s IP address and expose Jellyfin’s HTTP ports (e.g., 8080) - just make sure to not forward those ports from the router. You’ll have local unencrypted transfers if you do this, though.
Make sure you have secure passwords in Jellyfin. Note that you are vulnerable to a Jellyfin or Traefik vulnerability if one is found, so make sure to keep your software updated.
If you use Docker, I can share some config info with you on how to set this all up with Traefik, Jellyfin, and a dynamic dns services all up with docker-compose services.