Thank you for the additional information.
As you eluded to earlier, unless you have a charge coil to charge the battery, putting a battery in the system is going to make it a total loss system. I am well familiar with the Baja Designs light kits. If there is no surplus of amp flow, having a battery in the system is a very short term solution. All amp flow will be negative and it is just a matter of time before your battery dies. I do suspect it won't last very long either. The cable Suzuki uses to check the TPS will not be of any value when trying to add a battery into the electrical system. It merely supplies enough voltage to check the TPS.
As far as constructing a charge coil to use with the stator that would provide enough amp flow to produce positive amps at higher RPM's would be more trouble than it is worth, in my opinion. The new stators no longer separate out the various coils used where you might have a fighting chance to increase the output of one of them. The style of stator your bike has incorporates all the various windings around one laminated iron core.
Trusting Baja to know what they are talking about when they tell you the output of the stator is pretty much maxed out and being able to charge a battery isn't a great alternative either, you have few options other than forget the whole project or take a shot at it and see what happens. If the turn signals and brake light are more of a need than a want, you would probably have to forego those as well.
Current bikes just don't lend themselves well to re-engineering.
If you have to have all the lights of a street bike, you would probably save yourself a lot of grief by buying a street bike, perhaps like the DR650SE. If you need something lighter, they also make a DR200.
If you have any more questions feel free to ask.