Can I turn on every GPS, WIFI and Bluetooth radio of a mobile device and synchronize data transfers at extreme speeds between a small, short-range network of devices?
This question has several parts.
"Which radios in a typical mobile device can both transmit and receive?"
Typically they'll have Wifi, Bluetooth, CDMA/GSM, and LTE for recent devices. The other radios, GPS, for instance, are receive only and can't be used for communications.
"Can these radios be used for device to device communications?"
Yes, with limitations. For instance the cellular radios are often developed to transmit and receive in different portions of allocated spectrum, and tuned for that use to make the hardware development easier - smaller filters are usable where it is known that a receiver won't have to deal with the transmitter's power at the received frequency on the same device, for instance.
"Can I program the phone, perhaps jailbroken, to use these radios?"
In some limited ways, yes, but the actual software the radio modules run is not open and easy to reprogram. The phone's software, hidden as it is, is much more accessible to the average programmer than the radio baseband processor.
Trying to get the cellular module to talk to another nearby device with a cellular module, if the hardware makes it possible, may still be impractical or impossible depending on your knowledge and skills at programming radio baseband processors. You typically won't even be able to get complete datasheets for these modules without NDA's and promises of large orders from Broadcom and other chipset manufacturers.
"Can I attain extreme speeds using these radios?"
No more than they were designed for. Mobile devices are extraordinarily efficient in cost, space, and energy usage. They are designed exactly for the communications they intend to carry, and nothing else. You aren't going to magically squeeze more speed out of the wifi than it was designed for with "custom programming" or by somehow coupling them with synchronized multi-band radio communications. If your wifi chipset was designed for 108Mbps, the bluetooth for 263kbps, and the LTE for 1.1mbps, then you'll get, at most, 109Mbps total aggregate data transmission out of them, adding them together. "Synchronization" isn't going to allow you to double or triple the bluetooth throughput magically.
Software would intelligently select bytes for transfer at appropriate times estimating time of arrival on each spectrum with prioritization based on initial synchronization testing. Is this possible?
Sure, but for short distances it won't matter. Trying to synchronize the radios down to the bit timing might not be possible anyway, but even if it isn't, synchronization isn't an issue if you packetize everything.
Is this possible with a multi-antenna and multiband cellphone like a jailbroken iPhone A1533 or even A1530?
Anything is possible given enough time and resources. If you want to accomplish this without a team of engineers and access to all the datasheets and existing code of these devices in the next few years, though, I posit that it is practically impossible to fully accomplish your goal.
As far as "extreme speeds" newer devices are coming out with 802.11ac, which can attain what most people would refer to as "extreme speeds" starting at 433Mbps, and going up to 1.6Gbps per device. Further, these don't require any jailbreaking, hacking, or amateur radio licensing at all, these devices will talk directly to one another in short range situations using standard TCP/IP and have been FCC device licensed for consumer use.
Besides, the one fast radio, wifi, on these devices is two orders of magnitude faster than all the other radios on the device put together. Hacking the device and somehow adding them together will increase your communications speed by 1-2% over simply using the one wifi radio. I don't think there's any value in pursuing this investigation.
I'm not sure what you're trying to accomplish, but I hope this provides some direction for you in achieving your goal.
