I don't know if I trust myself to make that work. From watching my bench power supply with a bunch of USB powered things li ion, it stays constant current within the 0.001mA range then the last 20% of the time the current goes up slightly then down, as it approaches 0 the charger just stops suddenly. That seems very specific to use a LM317 and resistor.
The USB charge can be described as both current and voltage limited. If you limit the voltage to 4.2V per cell, then the only way it can exceed its own max charge rate is when it is discharged significantly. For sake of argument, let's say a given cell must be discharged at least halfway before connecting it to 4.2V constant voltage source will allow for a dangerously high current.
So for this particular cell, if it were completely discharged, the USB charge circuit/IC (that is custom tailored to charge it as fast as safely possible) would be limiting the charge current to a given amount up until the cell was halfway charged. At this point, there is no longer any need to limit the current. At this point, the charge current will naturally taper off because of ohms law. 4.2V-Vbat is going to decrease. And the internal resistance of this particular battery will cause it to draw only the max safe current at this halfway point; thereafter, the current will taper off as Vbat rises.
I am speculating that the current on the device you witnessed "rise at the last 20%" is because it used a simple series resistor or somesuch to initially limit the current rather than an active current control. Once Vbat reaches a safe level, it switched this passive limiting device out of circuit so that is would no longer unnecessarily reduce charge current. Thus the current draw spiked a little at this point.
The only reason a USB battery charger has to turn off at all is if the voltage is a bit higher than needed. If you used a charge voltage say 0.1V higher than the max voltage the cell can handle, you can get that last 10% of capacity to charge a bit faster. But you need to turn off the charger when Vbat reaches 4.2V. If you charge with 4.2V or less, there is no reason you can't just leave it on there, indefinitely. Also, the main reason the USB charge circuit has to detect when the cell is charged is so it can flip an output line which can be connected to an indicator light. So the user can watch a red LED turn to green, and know the cell is done charging.
The graph you will find in a typical (good active) charging IC datasheet represents the current passed in order to safely and practically charge a cell in the fastest time. There is no need to follow this curve. There is nothing magic about it. Your current graph can look totally different, if you are ok with a longer charge time. You just have to limit max current and keep voltage under and up to 4.2V.
Yes, there are different chemstries needing different voltages. And batteries with multiple cells in series will need some extra precautions (for instance, I charge one particular 4S pack I use to only 16.6V, instead of 16.8V for starters). But there is no special precaution (I'm aware of) to charge li ion cells in parallel. For all intents and purposes, charging 2, 3, or 100 (matching) li ion cells connected and used in parallel is no different than charging a single cell that happens to have the same construction but is 2, 3, or 100 times larger in size. The reason NiMh cells are squirrely to charge in parallel is because Vbat is not a function of SoC. As you charge a NiMh cell, Vbat will rise, then fall, then rise, again. At a given Vbat, there are multiple states of charge. In li ion, Vbat is a function of SoC. Thusly, if one cell has more charge than the other, this means Vbat is slightly higher. And current will flow from that cell to the other. Simply put, li ion cells are self-balancing, in parallel.