Adjusting mirrors is a battle you can't really win, even on a standard push bike.
Yes You Can win that battle...lol...I WON that battle, although I only use the one mirror on the left from the pair provided...I bought the pair for $11.99 though they are presently out of stock.
How I won the battle was pretty simple really...I threw out the cheesy plastic handlebar mount and then made my own mount using ordinary plumbers straping to wrap around the handlebar with very thin rubber underneath it by doubling it and then leave the larger holes protruding outward to put the threaded end of the mirror bar through it with a nut on one side all the way up to the end of the mirrors bar that is toward the mirror end and then the protruding end of the other end on the bottom end...
I then simply tightened the bottom one with a 10mm wrench till tight and then used my other 10mm wrench and tightened them against each other.
It's been on for two and a half years now and has not needed any retightening whatsoever...Since I have virtually no vibration by how my motor and chain drive mounted I can see clearly in my mirror what is behind me and the mirror itself on its pivot head is on so firm, it just doesn't move.
I previously had more expensive mirrors that always needed adjustment, These El Cheapo's I now have are a Godsend.
My speedometer is cranked down about as tight as it's going to get and still drops a bit when I hit a big bump.....
Your Speedo is probably one of those big heavyweight analog ones I am guessing.
The speedometer I am using is a digital one that is mounted using zip ties right smack dab in the middle on the handlebars on the handlebar mounting itself...It also does not budge.
These are not the clearest pics I have ever taken,...lol...but gives ya enough to see how I did it.