Is there any way to charge faster without a 220/240v outlet?
The simple answer is no; you always need 240 volts (220) to get a faster charge time. However, There is a product on the market from another vendor called a "Quick 220" which enables one to obtain 240 volts by using two standard 120 volt outlets that are on different circuits. This may not work for everyone, but in some situations this can be a possible route to faster level 2 charging. An example of this is say one has rental property and there is no possibility of installing a 240 volt outlet, but there are existing usable 120 volt outlets.
If you have a 2013 LEAF, You would need to order the appropriate Quick 220 device and an L6-30 adapter from: Quick 220 systems, (we recommend you contact them for details) and then program your EVSE to an amperage compatible with your outlets and circuits. This would then (at least) double the speed of your charging, and all without needing a 240 volt outlet. To be safe for operation on standard outlets, you should consult with an electrician, but the general rule is to set your EVSE's maximum amperage to 12 amps using these instructions. If you have 20 amp outlets, then you could set your EVSE to 16 amps maximum.