R4002 & others:
In essence when all is taken into account and given the due consideration it deserves it's just Indonesian pirate operators mucking about in a form of "Claytons CB Radio" in a world of Play Wireless etc.
Someone mentioned awhile back, it may have been you R4002 or Token, due to poor propagation on 25-30MHz a lot of "Freeband" style operators have made the migration south frequency wise (6MHz for example). More evident in Latin America and parts of EU.
Spectrum Anarchy is alive and well it seems with authorities in all countries concerned doing sweet FA about it. It amazes me how the Indonesians get away with it on the upper 8MHz aviation section. There is a group every opening on 8.831MHz yakking away with Flight Watch in Brisbane working traffic on same. 
The Indonesian version of the FCC would take years to clean them up, hundreds of isolated islands make up Indonesia, many don't have air services and rely on sporadic shipping services. Then again, with bribery and corruption part of the Indonesian culture in government many would be protected by way of financial back handers. 
I guess if an aircraft crashes and kills scores of passengers due to the pilot experiencing interference on the channel from the Indo's etc they may get off the clackers and actually do something?
What transceivers are they running? Converted amateur gear or cheap junk box 0-30MHz transceivers from China? Some of the Indonesian signals here are very strong and have excellent audio (ideal for chanting) suggesting good quality equipment. Very little bleed over/splatter noticed on many so quality gear?
Guess we can close the book on the Indonesian chanters, thanks all for your investigating, especially Omega who found info via the VKlogger, good research! 
In regards to the interference with aeronautical HF communications, I remember reading somewhere about the Cuban numbers station HM01 causing interference to one of the Caribbean sector frequencies and the controller had to request that all aircraft QSY to an alternate frequency. Although there's a difference between a 10 kHz wide AM signal transmitted at hundreds of kW and a SSB voice signal transmitted at the most maybe 1-2 kW (but probably more like 100 watts) but still.
I can say with 99% certainty that several of the Latin American operators I've heard chatting in the 6-7 MHz region have also been heard (by me, and likely a bunch of other people) on various 11 meter freeband frequencies. I've seen several YouTube videos of stations on some of these 11m free band frequencies, namely 26.225 MHz USB, 27.455 MHz USB and of course 27.555 MHz USB and they're using various higher-end HF amateur radio rigs, all the name brands can be found, Yaesu, Icom, Kenwood, Alinco, all the big ones. I know the markets are flooded with cheap Chinese CB radios that do 25.615-30.105 MHz out of the box, with more expensive ones doing SSB in addition to AM/FM.
Some of these guys are running HF equipment that would leave most ham operators jealous. Others are using open-banded "10 meter" radios and others are likely using marine SSB equipment or maybe even old military gear. I know there has to be at least some old HF military equipment floating around that part of the world, and most of the older-generation gear (for the US anyway) didn't even cover the whole 2-30 MHz band, some of it stopped at 12 MHz, others stopped at 18 MHz Vietnam War era HF military radios did have SSB (I think the more common ones only had USB/CW or USB/AM/CW, so that doesn't match with these guys using LSB).
Anyway, the AN/PRC-74, AN/PRC-74A (2-12 MHz) and the AN/PRC-74B as well as AN/PRC-74C (2-18 MHz) were USB/CW only, but can apparently be modified to transmit in LSB mode as well. Bigger base station military radios like the Collins series and the AN/GRC-106 radios (which
does cover 2-30 MHz, again only in USB/CW) transmit considerably higher power, up to 400 watts PEP SSB power for the GRC-106 HF radio. The more modern HF military equipment does 2-30 MHz in 1 kHz steps, often with LSB included on the mode switch...I don't see it as being to far-fetched for a village to have re-purposed surplus or simply left-behind military radio equipment for use as their "village radio".
Of course, its a lot easier to get a full band 160-10 meter HF ham radio, do the "freeband" or MARS/CAP mod, and then use any frequency you want. I think this is the most likely option. That, and at least some of these stations are licensed amateurs who use the amateur frequencies when they want to, and bootleg in the freeband frequencies (or, you know, the safety of life radio service frequencies...) when they want. As you mention, they're isolated and live in a world where cops are underpaid and corruption is common. There are lots of cheap junk box transceivers from China, but I haven't come across too many full band HF ones. "CB" equipment that covers roughly 25-30 MHz, and VHF/UHF equipment...well that's another story. I've seen several listings for radios on Chinese vendor's websites - a lot of these guys think "HF" is the 66-88 MHz VHF mid band, and "CB" is 25615-30105. Do a Google search for radios like the CRE 8900 (also known as the Alinco DR-135CB, Alinco DR-135UK, and Alinco DR-10), the Anytone AT-5555 series (known under about three dozen other brand names and model numbers), the Anytone AT-5555N (completely different radio from the AT-5555), Anytone AT-6666, Anytone Apollo II, the Nanfone radios, and dozens and dozens of other makes and models - all coming out of China.