many people have started dry tanks for shrimp. What I mean is they take filter media and a healthy portion of substrate from an established tank, along with some live plants, place it right in the tank and let the shrimp go. When I say established, I mean cycled with plenty of biofilm. This is a less than ideal way to start a shrimp tank but then again this is a less than ideal situation you have. The idea is to get as much biofilm into your new tank as possible to kickstart the cycle.
How many shrimp do you have? I found a similar thread with an Eheim 2213 in a 10g and the person was advised to just aim the outtake at a wall about 5 inches away to diffuse the flow (
the thread). It still sounds pretty strong if your shrimp are caught up in the flow. I know you said you didn't want to spring for a new filter if you could help it but consider a sponge filter like this
Hydro Sponge 1, especially if you have a spare air pump laying around. You can also find quite a few DIY instructions for sponge filters if you're the handy type.
Be aware that while your shrimp can survive this Dry Start method the tank will be like a desert for them. Normally shrimp will constanly graze on infusoria in an established, cycled, mature tank. Since your tank isn't set up yet, there's not yet any infusoria. If you do try this Dry Start, be sure to keep up with frequent partial water changes. Best of luck to you and keep us updated, please
edit: borrow media and substrate from the unmedicated betta tank, and don't worry about the finrot as far as the shrimp are concerned (no fins means no finrot)