Deerslayer,
Good questions. My understanding is that US-made copper plumbing pipe contains about 0.02% phosphorous, which is probably not enough to cause a discernable change in the rate of dissolution of the copper into the molten lead, or in the properties of the resulting lead alloy. As you know, phophorus deoxidizes copper at melting temps, but since dissolution does not entail melting of the copper, the phosporus may not convey any significant advantage during dissolution. I think that tinning is likely to be the quickest route to dissolution. Any old tin/lead solder, and some rosin, will 'tin' the copper.
In greater amounts, I suspect that phosporus may possibly increase the solubility of copper in lead. Cu/P brazing alloy, with several percent P might offer some interesting opportunities for Pb/Cu alloy experimentation. Also, see post #28 in this thread for a little more commentary on phosphorus in Pb/Cu alloys.
Regards, and good shooting.