I'm sorry but I'd prefer not to go into this right now unless the tester him/herself has such specific questions, I'm just getting an idea of what procedures would be acceptable. It looks like I'll have to be in direct contact with an official tester by e-mail or phone rather than relying on a time stamp as proof, so this could be a little tricky. What makes a test more feasible is that any tester wouldn't have to do anything, just check their email or voicemail during a period of a few hours to verify.
As I said previously, for a real test you will have to be there in person. No matter how much you try, you will never get the internet or phone lines secure enough for someone to bet a million that you can't be cheating, as well as needing to have people present as observers and usually recording as well. This internet and encryption business is all very well for an informal test, but you cannot assume that your real test will be at all the same.
Why is it such a problem for you to take a normal test? Where do you live? There are skeptical organisations in almost every country with members who would be happy to spend a couple of hours running a test properly. The JREF tests do not have to be run by Randi, and in fact he stays out of it so people can't accuse him of cheating, they are run by representatives of the JREF who are usually chosen from local skeptic organisations.
As I see it, a suitable protocol would be as follows :
You sit in one room, the person rolling the dice, who must be approved by you, sits in another. No contact can be possible, by any means, between the two rooms. A minimum of two observers, approved by both parties, are required, one for each room. Preferably four observers would be present, one chosen by each party in each room so that no-one can accuse anyone of forcing an observer on the other. A final person will act as a courier to take the results of the dice rolls and your predictions. Both rooms will be continuously recorded in both video and audio. No person other than the courier may leave a room at any point, if they do so the test is null and void. No communication devices will be allowed to anyone, again, the test is void if any is found after the test has begun. Ideally you would sit in a Faraday cage to prevent any possibility of electronic communication, although this is unlikely to be possible.
For the test, the dice will be rolled to obtain a number from 00-99. The courier will write this number down and place it in a sealed envelope labelled with "Roll" and the test number. They will carry it to the other room and leave it, untouched, on a table. They will then leave the room. You will then make your guess at the number. Your guess will be written down and placed in another sealed envelope labelled "Prediction" and the test number, and then placed with the roll envelope. The courier will now be signalled, by knocking on the door for example, to go back to the dice room for the next roll. This will continue until the required number of rolls have been made. Until the test is over no-one other than the courier may touch the envelopes and there will be no feedback of any kind to indicate your success on previous rolls.
Once the test is finished, the envelopes will be opened. Everybody should be present for this, since there will be both your observers and the skeptic observers who have seen both results and will therefore know that they haven't been tampered with. A score of 3/3 would be obtained with 1:1,000,000 probablility, but it is likely that more tests would be run and less than 100% accuracy would be required. The exact score that constitutes a pass must be worked out between you and the JREF beforehand.
Ideally the courier would be two people, one chosen by you and one skeptic. If required the envelopes could be kept in a third room with two more observers to watch over them, although this is probably overkill and as long as the numbers cannot be seen through the envelopes is probably not needed.
This simple test only needs five people, you and four others. Ideally, and especially to cover your concerns rather than the testers, it would take eight, you, three of your friends and four skeptics. A location could be a scout hut or church hall which could probably be obtained free for the short time required. It should only take two hours at a generous maximum. Even someone's house could be used, although this might not be acceptable to the JREF. It should not be difficult for you to find three friends, and it should easily be possible for a skeptical organisation to find four people close to you, so there really seems no reason to fuss over internet and phone protocols when it is so simple to conduct a real, secure test.