Following are my results of trying five various ROMs on a StraightTalk SCH-968C with the H1 baseband. I DO NOT have a SIM card available, nor do I have a friend or family member that I can borrow one from, nor do I intend to buy a new/used SIM card. I'm using CWM 6.0.4.5, which works great on this phone. I need to have both MMS messaging AND the camera working, because I use both of those apps, and that's what we seem to be having issues with. MMS was tested sending and receiving with another StraightTalk CDMA phone (a Motorola Moto something...) Disclaimer: If you try to duplicate my efforts and end up bricking or otherwise screw up your phone, I will not be held liable. Your results may vary...
I first tried CyanogenMod 10.2.1 (cm-10.2.1-d2vzw). Unknown network, Mobile network type: CDMA-1xRTT, in service, Disconnected from mobile network, unknown phone number, unknown MIN. That's all I checked before shutting down the phone. Two days later, I boot up and there's no cell service at all. Wiped it off the phone. This is the only ROM of the five ROMs in which after I restored the stock ROM from backup, I still had no cell service. I had to go into 'Settings', 'Back up and reset', and do a 'Factory data reset'. When the phone rebooted and the reset finished, the cell service was restored.
I also tried CyanogenMod 10.1.3 (cm-10.1.3-d2vzw). After install, I had cell service, but "no data". The stock messaging app didn't work with MMS. Chomp SMS - kinda... Some MMS messages were sent/received after a delay of 10 minutes, some were sent/received after a re-boot or a force-stop of the stock messaging app. Neither the stock camera app nor Open Camera worked. (Can't connect to the camera.) Three strikes - this ROM is history.
I then tried AOKP (aokp_d2vzw_jb-mr2_milestone-1). Get this: the stock messaging app worked with MMS messages! Once again, neither the stock camera app nor Open Camera worked. (Can't connect to the camera.) The camera wouldn't work, so off it goes into the bit-bucket...
The I tried OmniROM 4.4.3 - (omni-4.4.3-20140620-d2lte). The stock messaging app wouldn't work with MMS, but Chomp SMS did. And as before, neither the stock camera app nor Open Camera worked. (Can't connect to the camera.) This ROM goes into the bit-bucket too.
Last, but not least, I installed SlimKat (Slim-d2lte-4.4.4). The stock messaging app didn't do MMS, but Chomp SMS did. And guess what?! - the stock camera worked great! I was going to keep using this ROM, until a couple of days later when I was trying to install some root-required apps, the ROM didn't recognize that my phone had been rooted. Root Check didn't even recognize that the phone had been rooted! So I once again had to wipe and restore my stock-ROM backup.
In summary, I can't get any of the major ROMs to reliably work with the H1 version of the SCH-968C. When a ROM is released that is specifically for this phone and all features will work AND it doesn't require a SIM card, I'll gladly try it.