The only method that is possibly a tad cheaper is to get the wheels tested by TÜV Austria (A subsidiary of our TÜV that is seemingly a bit more flexible. The certificates are recognized here as well.)
What you've described here is the unfortunate reality of what anyone has to go through to enter the German market.
I'm not speaking for all GR Yaris owners here but I'd think that a 18x9 ET45 would be very popular. ProTrack Wheels is selling a bunch of wheels in that size to a lot of German owners that like tracking their car. Other sizes I would personally take into consideration fo the Yaris are stock size 8x18 ET45 and perhaps the 8.5x18 ET45 of the GRMN wheels.
If you do end up deciding to go for it I would strongly recommend going for a Teilegutachten (Parts certificate, it's inbetween a type approval and a simple strength certificate) as that really takes the difficulty out of getting the parts homologated on our cars and an Allgemeine Betriebserlaubnis (Type Approval..) isn't compatible with other tuning components that might affect the performance (see coilovers which a lot of people are running) so people would have to have their car inspected by an Engineer anyway.
If you do end up going that route, please register my interest for an 18x9 ET45 set