What about tying the ends together on the position they are on the picture (so within the frame triangle just under the seat tube), then some trousers belts, wrapped as much as their length allows, diagonally around the frame tubes joint there? It will even be stronger, only somewhat less stiff.
The entire luggage backside of my bikes frame (see my avatar) is held together by that.
Benefit is, if it all suffers a hit, it can move a bit to absorb the energy instead of breaking.
Something important: make sure the movement can't cause fretting in the frame. Inner tube rubber is ideally to prevent, it can absorb energy itself too, is antislip, and allows a tight knot.
Here, 40 kg loaded on top of such belts-connected pannier frame.
When such heavy loads, I connect the rear wheel frame tubes additionally, in order to offload the pannier frame bolts abit.
By the way, how did it break? It's not that they're that weak, and actually, they don't have to take the luggage load, only the horizontal component of it which is much smaller since bicycles speed changes are not that big eh.