I have the Shorai also, and really like it. A battery should not go bad sitting for a week. If it does, you either have a bad battery, or a parasitic drain. The Reg/Rec is not involved in the storage capacity of a battery. I still like the more modern Reg/Rec, just because I prefer modern electronics. Theres nothing at all wrong with the stock units, but if you are motivated to replace items, that is one that does get replaced frequently.
BEFORE you replace the Reg/Rec lets sort out your battery issue. The proper test is to fully charge your battery, then allow it to rest, off the charger, for at least 2 hours. Compare the voltage between "fully" charged and "after a rest". There should be no appreciable drop. For a standard lead acid, you will see about 12.4-12.8v. With the Shorai, you will see 13.2, 13.4 and all the way up to 13.8v.
Now for the Reg/Rec: understand its function so you can clearly diagnose any problems in the future. It (the R/R) sits between the battery and the alternator. It measures the state of the charge in the battery while the bike is running, and metes charge from the alternator to the battery. When the battery is depleted, it allows more charge to reach the battery. When the battery is full, to throttles the alternator's output from reaching the battery. Hence, "regulation".
An alternator left "unchecked" by a R/R will over-charge your battery, throwing as much as 15+v at the battery. That will cook your battery instantly. So, once your battery is installed, and verified "good", then install the R/R and verify the following:
Voltage at the following RPMs-
2,000
3,000
4,000
5,000
The voltage read from the battery (meter on + and - terminals) should never exceed 14.8v with a Lithium battery. If you see more voltage than that, your R/R is not properly wired. You should see from 2,000 RPMs voltage around 11.8-12.4, and then climbing with each 1,000 RPMs. This is verification the alternator is functioning. What remains is whether the R/R is properly managing the output, and whether the battery is successfully capturing and storing the voltage. Make sense?
For eliminating electrical problems, step-by-step is really the only way to isolate what is wrong, then correct it. If you change numerous things simultaneously, you will chase your tail for a while.
All of the above is predicated on good, solid ground connections, clean connections between all circuits, and no unusually high resistance in the harness (resistance is produced by corrosion as a by product of poor continuity as an example). If you really want to insure that you are solving your problems, grab a decent multimeter and lets start checking stuff before changing it. It will only take a little while, but will pay huge dividends every mile you wish to drive!