We have a winter place in Bangkok, so I know a bit about the services there. Though there is very little free Wi-Fi, the carriers, especially True and DTAC, have a huge number of (paid) hotspots, access to which is included with many of the phone plans. I'll try to answer any other questions you may have about service there. I've never been to Cambodia or Vietnam. My limited experience in Japan and China was before smartphones became popular; I used commercial callback services to make calls. You can also set up the OBi to do callback, using any service you like.
If your Android phone is on AT&T or T-Mobile (i.e. it's a GSM model) and is unlocked (get unlock code from your carrier if you've had an account in good standing for awhile, or root and unlock it yourself), a SIM such as this may meet your needs:
http://www.truemove.com/en/Inter-SIM-Prepay.rails .
Both OBiAPP and OBiON register to an OBiTalk server, as does your OBi device; the system does not depend on being on the same LAN. You can test this by connecting at a friend's or at a local hotspot. Possibly, your audio problem with one-stage dialing was related to trying to bypass the Internet and it will work ok when the clients are on a different network.
Alternatively, you can connect to the OBi via a SIP service; a free PBXes account may meet your needs. My setup has the OBi as a sub-PBX and can do one-stage dialing. Also, PBXes can fork incoming calls to multiple clients.
For non-VoIP calls to your cellphone, you can have the OBi bridge the call. Using GV to Thai mobile is $0.03/min. There are of course lower cost alternatives, such as CallWithUs or a Betamax brand.
You might get a PSTN DID that forwards to your mobile, e.g. Callcentric, Anveo or Localphone, which would avoid dependence on the OBi, at somewhat higher cost.