I say go ahead and mix them like you have planned.
Not only will it not be terrible for the 8AH, it will help the 12AH.
It wouldn't be as ideal as one string of 20AH batteries, but you knew that.
The 8AH will NOT drain faster than the 12AH. They will be in parallel. It will take exactly the same time for the 8AH and the 12AH to go from 12.7V (full) each to 11.9V (empty) each.
Say the thing runs 1 hour with the 12AH batteries, it is draining them at C/1, or 12A.
That is hard on batteries, naturally. Completely full to completely empty in 1 hour!
The motor still will only drain at 12A with both sets paralleled. But the capacity is now 20AH. The drain is now much less related to the capacity.
Now the batteries go from completely full to completely empty in 1 hour and 40 minutes.
Three good things come from that...
The battery abuse is less because the drain is reduced to C/1.67 and the batteries will have more life cycles.
The rated battery capacity will be higher because AH rating goes up as the drain goes down.
To the store and back will leave the batteries at a higher voltage, meaning less deep cycling or DOD.
Just because the draw is 12A doesn't mean it will take 6A from each battery string. That would mean the 12AH batteries take 2 hours to go dead, but the 8AH batteries are dead in an hour and 15 minutes. They are parallel and the voltage will always be the same.
A bad battery in one string will drain the other string because the voltages must be the same. The good string tries to charge the bad string.
Kirchoff. What a guy!
G-