to answer your original question. the reason for 14S as the limit on the balancing charger is because the mosfet used for switching is rated to 55V.
you should remove the lipo from the shrink wrap if you build a battery up from HK packs and remove the heavy plastic tape wrapped around it over the top and bottom and then solder the top of the lower pack to the bottom of the upper pack with a short solid 12AWG copper wire and remove the big 10AWG silicone wire altogether. remove the HK JST plugs and wires, and then solder on the BMS sense wires. order some 9 pin plugs off ebay to plug the cellogs into and solder those leads to the battery or the BMS sense wire plug pins on the BMS.
the shrink wrap and tape distort the lipo packs and damage them so the lipo battery should be built just like ping builds his lifepo4 packs, except instead of shrink wrap you should use 1/8" hardboard end plates the size of the pouches, compress with a clamp, and then wrap the entire assembly in duck tape while it is compressed. that will help get the longest cycle life from the lipo packs.
the BMS will protect from shorts on the output and from over discharge and it will allow the pack to balance under the bulk charger, just like the balancing chargers.