How to remove glossy paper residue from copper and toner?

I hope that someone will suggest a way to make it easier to remove the residue from glossy paper that is left on copper-clad printed
circuit boards (pcb) and on laser printer toner, after I heat-laminate a circuit pattern (i.e. toner) from glossy paper onto a pcb [See , for the exact procedures and materials used (with photos), if you're interested.]
Briefly: After printing the artwork for a circuit board's copper pattern onto glossy (i.e. coated) paper, with a laser printer, I use a clothes iron or heated laminating press (350+ degF) to transfer the toner from the glossy paper onto a thin sheet of copper-clad fiberglass (the "blank" pcb). The etchants (Ferric Chloride, or, Ammonium or Sodium Persulfate) will eat copper but not plastic. And laser printer toner is made mostly of plastic. So the desired copper circuit pattern remains, under the protective toner, after the rest of the copper has been etched away. A quick wipe with acetone or lacquer thinner and it's ready to drill and plate with tin and then populate with electronic components.
That all works quite well. But, after heat-laminating the paper and toner to the copper board, it is very difficult to remove the last bits of the paper residue (and/or its coating?), which must be removed prior to etching since it interferes with the etching process.
Specifically, just after laminating, I soak the board, with the paper still attached, in hot tap water, until the top layers of the paper can be rubbed off, fairly easily. Most of the remaining paper residue comes off pretty well, with a lot of rubbing, or scrubbing with a toothbrush (which would also be nice to be able to avoid). And the toner stays put. However, it is usually VERY difficult to remove the paper's residue from the tiny drill-holes that were drawn in the pattern, which are 0.02-inch squares without toner that are in the middle of an area that does have toner.
I am hoping that there is some common (or not) chemical or procedure that I can use to dissolve or loosen the paper residue, without doing much harm to the toner, the copper, or the fiberglass.
I am not sure what the glossy paper is coated with, that makes it glossy. It might be clay. I am using "Staples Picture Paper", from the "Staples" office-supply store chain, in the USA. Some other glossy papers come off VERY easily, after laminating onto a pcb. But I haven't found a paper that comes off easily that also accepts images without leaving pinholes in the toner.
Any helpful ideas would be GREATLY appreciated.
Tom Gootee
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