I open this topic since I had some trouble with the border crossing permit, to leave Myanmar to India by land (Tamu-Moreh border). Hopefully it can help (near-)future travellers.
So far I've been told these agencies and that's my experience sofar:
-Exotic Myanmar Travel:
Normally it should take about 20 days to get the permit, so it should be applied in the first 8 days of stay in Myanmar (for normal 28 days tourist visa). I went to the office on my 6th day in Myanmar quite in a hurry, on February 6th, and the guy told me that because of chinese new year holiday it will take longer as 20 days, so they gave me date for March 2nd or 3rd (!!??). My visa already expires on February 28th! It's only 3$ of "fine" for each overstay in Myanmar, but I preffer to avoid trouble.
Price for this agency is 80$. The guy's english wasn't that good.
-Seven Diamonds Tour Agency:
After riding across half Yangon in its crazy traffic, I got to the Seven Diamonds office. This agency was my "joker", since it was quicker than the Exotic Myanmar Travel, but more expensive. They told me that they don't do permits anymore! I asked them for how long, and they don't know, but it seems long term. I managed to get the contact of another agency: Journeys.
Price for this one used to be 100$. Their english was good, but what for? hehe.
I called the agency, but it was saturday and they were not working. They told me that they will call me on monday to give me more information, as normally they only offer tour packages, and not just the permit. I told them that my visa expires on 28th, and the guy on the telephone told me it's ok, we have time.
On monday after some calls they told me that I can't get only the permit with them, that I need to book "something" with them, like hotel or similar. I asked them how much would it be to get the permit and the cheapest hotel night for February 27th, and they just told me that 27th is too early, that they can't do it that quick.
I couldn't get the price.
I was told about this agency by a french couple that heard about it, and that it should cost only 50$. Couldn't get in touch with that agency...
-Ministery of Hotels & Tourism
I called them and the woman's english was really poor, so my hostel's reception talked to them. Apparently the guy who should do the permit is on holiday for 10 days and couldn't get more information.
In the end, after all that, I tried to go back to Exotic Myanmar on February 8th and talked to a different woman. This time she told me February 27th will be ok..., so I paid 80 bloody USD. I had two stressed days for nothing, but it's alright.
So, that's my story, salut!