Hi,
I've ticketed your issue as https://github.com/OSGeo/gdal/issues/8672 .
What you could try to reduce the execution time is to enable
multithreading by adding -wo NUM_THREADS=ALL_CPUS to your gdalwarp
command line
And yes the previous implementation of the raster TPS transformation was
"
https://raw.githubusercontent.com/craigshelley/QuickChart/master/Specification/The%20Quick%20Chart%20File%20Format%20Specification%201.03.pdf
describes a file format which includes polynomials describing forward
*and reverse* tranforms for this.
I don't know how common, or accurate, such reverse
