This type of charger balances very slowly. These are way out of balance so it will take a very long time to balance them. Most chargers are made this way, they series charge and then bleed balance the fully charged cells, then repeat to bring the low cells up. The bleed balance currents are not very high and they alternate charging and then bleeding the cells, which is a slow way to do the job.
Charging each parallel cell group individually (but at the same time) would be much faster, this way there is no time spent bleeding. Some chargers work this way, charge through the balance leads and will do up to 6 or 9 cells at a time. The 9 cell type would work with your existing 6/8S wiring, the 6 cell types would require changing balance wiring to something like 6/6/2. Examples of these isolated per-cell balance chargers are (as far as I know this is a complete list):
BC168 (6 cell)
UN-A6 (Plus) (6 cell)
UN-A9 (Plus) (9 cell)
Radiolink CB86 Plus (6 cell)
Or, as you suggest, use this charger wired to charge 1S and use it 14 times, once for each cell group. When charging through the balance leads keep the current down to a low value that won't heat the small wires and connectors. I generally use 2 amps max.
Once the pack is balanced the iCharger should be able to re-balance it in a reasonable time, as long as the cells are well matched and don't get way out of balance again somehow.