you could try a bimini twist with an albright, but I suspect that it will impeed castability.
Im surprised that a double uni is "cutting" through - I use that to join platypus super braid (4lb) to 4 - 6lb mono leader and if any braid will cut Im sure that will, its like frickin razor wire!
Do you adequately lubricate (ie. slobber all over) your knots before tensioning them? Inadequate lubing can have the effect you are describing.
And are the lines of fairly similar diameter? If they arent, the knots mentioned will not work so well and the knot will "pull itself undone" so to speak.