If you want a regulated mod, and want low voltage, you need to look into vv, it's the only way I know of. Otherwise, unregulated batteries will have a usage curve. They start out at 4.2 volts, quickly go down to about 3.7/3.6 volts and stay there most of the time, then drop to cut-off voltage. The only way to avoid that is the regulation that you asked about.... and then you need a regulated PV. vv will let you dial voltage lower then the standard 5 volt regulated mods. Maybe not all the way down, but it varies depending on design. You'd have to check the specks, I'm not an expert on all the vv mods out there. Some are buck/boost and can take 1 large battery, most are probably dual battery designs.
The other option, due to costs, is to switch to higher ohm atties and standard regulated 5 volts (I know you said 3.7 but there's only so many regulated options). A static 5 volt mod is less expensive than vv as a general rule.
Also, MadVapes sells a box mod kit "on the cheap"... there's a post about it somewhere... if you want to experiment with vv. I just vape 5 volts static with 3.0 ohm atties and don't have to worry about it.... I'll probably try the vv someday when this mod dies.