You could reduce the problem somewhat very cheaply AND save energy by
insulating the outbound pipe on the water heater. You can get
fiberglass strip specially made for the purpose for a few dollars from
a home improvement/hardware store. Use latex gloves to avoid itchiness,
and keep in place with bag or cable ties, not tape. A slightly snug
wrap is best. Go at least to the wall, going further is your choice but
will be difficult and give you a diminishing rate of return.
I also use the leftover fiberglass to insulate the incoming pipe, an
amazing amount of heat leaks out that way and wrapping it preheats the
incoming water, saving you energy.
I also agree with collecting the start water in a bucket and using it
to flush, these low-flush toilets don't use enough water to get the job
done anyway.-Jitney