With an eternity band you are sizing up by the diameter of one stone ( or more as needed) and, while you can put in a bar, it somewhat defeats the effort of creating symmetry. One can also sleeve the ring down with very thin sheet stock, ( I prefer platinum) and simply swedge it in, or very gently heat the gold, it will expand, and the platinum will slip right in, when the gold cools and shrinks the platinum will nor come out.
If the ring is all platinum, chamfer the inside edges of the ring, sleeve, and take a large dapping die and tap the edges over the radius. To size up, again, the one stone rule (+ as needed) then sleeve back to the ideal side.
Laser will work, as will 1000 degree plat solder... If you're really brave, 1100 degree will work too. Come in from the back, make sure the fit Is exact, use a burnisher to work the surface and the solder line will be ( nearly) imperceptible .