I bypassed the heater core on a friend's LX. I was able to force the 5/8" i.d. hose over the larger tube. The hose was pretty warm at the time and that helped it give a bit.
You could probably use a hose clamp to keep the larger hose tight on the smaller tube, but that would be a very temporary fix.
Jrichker's plan is the best, long-term solution.