A good safety is to add a stopper knot to the tail end. This stopper could also be hit with glue since it doesn't normally take the load, or a fraction at most. Some sailing mag once had a "new" or "alternative" knots article and about half of them were simple knot + stopper combos.
The OP did tape the rope back on itself, the tape could weaken or tear with repeated loosen-tighten cycles but otherwise should help keep the pieces in the right position when it is pulled tight. Instead of tape one can also wrap the ends with smaller line (when this is used to keep rope from unraveling or as a replacement for a knot it is called "whipping").