Does anyone know of any alternatives to these that can be used without drilling them into the walls?

There's glue in a tube (you'd need a gun) and it goes by various names - it's called Hard as Nails over here.
You'd put some blobs on the boards, push them to the wall, support them for 24 hours and hey presto! Job done!
I'll see if I can find a pic
https://www.amazon.co.uk/UniBond-More-Nails-Original-Mini/dp/B004743I18

Presumably you have to be able to remove the board without damaging the wall at some future date - if so then glues aren't really an option as a glue capable of holding it up will take a chunk out of the plaster when you remove the board.

If you aren't allowed to damage the wall then it will be difficult due to the weight of the boards. Perhaps if you support them on something else and use blu-tack to stick them to the wall they might stay attached.

I'm sorta shocked that the heavy-duty command strips aren't doing it (maybe multiples? one to each corner?). does the wall/surface need some sort of cleaning to let the strip get to something solid?

I been try many of those so call nails free hooks,it all only works on tile.For wall it will tear apart pain and fall off over time.

I bet you could find something on the topic on YouTube. Maybe something that pins 📍 into the wall.

This stuff is supposed to hold up to 2lbs (a little less than a kilogram).

https://www.amazon.com/Gorilla-Removable-Mounting-Putty-Off-White/dp/B0873Z7Y42/ref=asc_df_B0873Z7Y42/?tag=hyprod-20&linkCode=df0&hvadid=459526850849&hvpos=&hvnetw=g&hvrand=5032998121177543032&hvpone=&hvptwo=&hvqmt=&hvdev=c&hvdvcmdl=&hvlocint=&hvlocphy=9030139&hvtargid=pla-942679609382&psc=1

The sticky hooks might work as seen on tv lol

Maybe Tesa Adhesive Nails?

How much do the mirrors weigh?