Short answer: you're doing it wrong. Do what I (and other members) said in previous posts on how to use CC inbound DIDs with GV and OBi.
TL:DR answer:
There are several errors in your conclusions, based on an incomplete understanding of what's going on. True, you can log into Google Chat with as many clients as you like, and make OUTbound calls with any of them. However, as long as you leave call forwarding to your Chat destination enabled in multiple client sessions (as I will explain below), you will have all sorts of unpredictable problems RECEIVING calls on your multiple destinations.
This sentence is one example: "However, with it turned off, neither box will ring with an inbound call to the GV number."
First, your interpretation of the behavior when the Chat box is checked or not is a common (and not obvious at all) mistake. This has nothing to do with Hangouts.
Among all the many confusing and undocumented aspects of GV, one issue is that multiple settings control which "forwarding destinations" will ring when a call to your GV number is made. You can remove the check mark as you did, but that setting is overridden by two other settings, in hierarchical order: Look on the "Groups & Circles" tab of settings, and edit each group or circle. You'll see a list of forwarding destinations. Even though you de-selected Chat on the Phones tab, it's still selected on the settings for any defined group or circle. So, you have to also change it there. Then, settings you may define for any individual contact will further override settings for groups, which override the setting on the Phones tab. Confused yet?
Next: aside from the previously-quoted sentence, your entire paragraph quoted below makes me think you either didn't understand my last post, or you don't understand how to configure your GV and OBi accounts.
As part of the configuration with CC, the GV account must have the Google Chat forward turned off - otherwise, as you stated, there will be contention between the two boxes. However, with it turned off, neither box will ring with an inbound call to the GV number. The CC forward (unique number for each box) is what makes each box ring. The outbound (SP1) is still GV on both boxes, as GV doesn't seem to object to multiple boxes initiating a call on the same GV account.
I tried to explain that, on GV settings, you need to have the GV Chat destination DISabled, and the CC DID destinations ENabled. GV will then forward calls to the CC DIDs defined on your OBi(s), and thus ring the phone attached to the OBi.
Here is how it SHOULD be done (as documented in more detail, several times in other threads):
Disable Chat as a forwarding destination on ALL three of the places I described above.
If not already added on GV Phones Settings, add and verify your Callcentric DID(s) as forwarding destinations.
On your Callcentric account, do NOT forward your CC DID anywhere other than the default (to a SIP client, logged in with your CC SIP credentials). Either disable CC's own voicemail system, or set its ring delay to 35 seconds or longer.
Assuming you have SP2 on your OBi(s) properly configured to answer calls made to the Callcentric DID(s), test this by calling directly to your CC numbers from some other phone. It should ring on your OBi(s). Then, call your GV number from some other phone. GV should forward the call to the CC number, which rings on the OBi on SP2. SP1 should NOT be getting the call at all. In fact, you should (temporarily) disable SP1 to test this.
The benefit of this, as you may know, is that you will receive caller ID name with the calls, a function that GV doesn't support natively.
Sorry this is so long and complex. If you do not understand what I am saying, please let me know.