Bicycle Mechanics - Canti Brakes on Step-Through Frame

I'm fixing up a step-through frame that has cantilever brakes. I'm having quite a bit of trouble getting the rear brake right. The cable routing goes from the lever along the down tube, under the bottom bracket, up the seat tube and over a pulley before it gets to the straddle cable hanger.

When I get the brake adjusted, there's so much springiness in the cable as it goes over the pulley that the lever uses about half its pull distance just taking out the springiness before it starts taking up any cable to actually actuate the brake. The lever ends up bottoming out before the brake is applied fully.

I'm using the brakes that were on the bike, but with different levers. The levers I'm using came off a bike with cantis as well. I'm assuming they would be appropriate for this use.

I've thought of taking the cable off and prebending it in the area where it passes over the pulley. Other than that, I'm not sure what to try. Any suggestions or tips would be greatly appreciated.

So there are bosses for V/Cantilevers on the frame?
and they are on the seat stay?

I have seen cable runs under the lowered top tube,
but never under the down tube. is this a mono tube frame?

a braided brake cable may go around all the bends better than the tight twisted cables.

I'd suggest the best brake: Magura hydrostop, its the hydraulic rim brake.
so as the braking force is a fluid, it won't be effected
by circuitous routes to get there.. fits on V/canti bosses..
German Made.

So there are bosses for V/Cantilevers on the frame?
and they are on the seat stay?

I have seen cable runs under the lowered top tube,
but never under the down tube. is this a mono tube frame?

a braided brake cable may go around all the bends better than the tight twisted cables.

I'd suggest the best brake: Magura hydrostop, its the hydraulic rim brake.
so as the braking force is a fluid, it won't be effected
by circuitous routes to get there.. fits on V/canti bosses..
German Made.

I'm at work, and the bike is at home. However, on second thought I think you're right. The rear brake cable runs under the lowered top tube and doesn't go under the bottom bracket. There are bosses at the top and bottom of the lowered top tube as well as a boss on the seat tube. There is a short section of cable housing between the bottom boss on the top tube and the boss on the seat tube. This facilitates the transition from basically horizontal to vertical as the cable runs up the seat tube to the pulley.

This bike is a low-budget build for a friend, so I would like to be able to work it out without adding any different components. Is the braided cable readily available at bike shops?

Is the braided cable readily available at bike shops?

may require special ordering, or I may be in nostalgia mode,
and remembering when it was so :50:

coiling the cable may be your only recourse , to be pre bent at the roller.

maybe pick up some V brake cable rubber seals,
upturned sections of housing are famous for retaining water, inside.

It's the pulley that sounds like it's the problem. I'm guessing that if you tension up the cable so it's tight enough to form around the pulley well then the cable tension is too tight and it causes the caliper arms to remain in and drag the pads on the rim. If this is the case I think I'd look at a seat post cable hanger to replace the pulley so that you could use housing from the sloping tube cable stop all the way to the seat post anchor mounted stop. The cable would then exit and go right into the straddle cable clamp.

In the end this sounds like a rather complex sort of setup. Some pictures of the cable path and especially around this troublesome pulley would greatly aid in suggesting options for you.