I’m in a similar situation as you.

I’m actually going to build a large platform (4x8) and hopefully the larger area will better distribute the weight.

I looked at rocker plates but they were $$$ and didn’t want to mess with a DIY.

I have a one piece mat that I bought from this website:
https://www.rubberflooringinc.com/gym-mat/shock-mats.html

Very heavy. Weighs 100 lbs and cumbersome to move so get it in place before you unwrap it. I have a cycleops hammer and ride a speed concept and madone on it without any issues.

Borrow from the audio visual world and google “speaker spikes.” These are put on the bottom of floor speakers to go through carpet and directly touch the floor underneath, for better support and acoustics.

In your case, I would install these spikes on some kind of plywood platform that goes under your trainer. Even if the platform is touching the carpet, it’ll actually be resting on the spikes. I’m not sure how many spikes you’ll need to install because I’m trying to be creative here, but I do know that spikes vary on how sharp the tips are.

If you decide to try this out, let us know if it works.

Sheet of plywood on the carpet, trainer mat on the plywood. The weight of the trainer/bike/rider should cause the carpet underneath to mat down.

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ECMGN Therapy Silicon Valley:
Depression, Neurocognitive problems, Dementias (Testing and Evaluation), Trauma and PTSD, Traumatic Brain Injury (TBI)

I used 3/4" particle board. A 4' X 8' sheet costs $21 at Home Depot. Have them cut it (save time, effort and mess) to a 3' X 5' piece. It will weigh about 50 lbs. and be very stable. I covered mine with cheap grey vinyl tiles - easy to clean up the sweat so no "locker room stink" (or just brush on a sealing coat). Put a few square feet of dense black gym/garage floor matt under the trainer legs and one smaller piece under the front wheel block to balance out and prevent "walking". Mine works great.