I continued my research on possible routes through the countries and found more about it.
Truly, there is an open border from Myanmar to India, despite of WikiTravel not being decisively positive on this: Crossing into or out of Myanmar proper by land varies between difficult and impossible. A land border crossing exists between India and Myanmar at Moreh/Tamu. While there have been confirmed reports of some travellers crossing into Myanmar from India, with their own transport as well as with permits arranged in advance, the general consensus is that obtaining all the necessary permits is very hard. At the least, a foreign (a person who is neither a citizen of India nor a citizen of Myanmar) will need to get a Indian permit to visit the state of Manipur, and an MTT permit to enter or leave Myanmar at Tamu. Travellers may also need a permit to travel from Tamu to Kalewa, although there are unconfirmed reports that this is no longer required.
Generally about getting a visa to Myanmar:
Some additional restrictions, requirements or conditions may be applied to applications - reports have included a need for a detailed itinerary, a detailed job history, etc. be prepared for some unusual questions (either on the forms, or from the Consulate staff) when applying for your visa.
The period of validity for the visa is rather wide:
Tourist visas are issued for a single entry, valid for two months from the date of issue. The visa is good for a stay of up to four weeks (from date of entry). Successful applicants will also be issued an "Arrival Form".
My point is that I will have to get used to the fact that there are borders that I won't know the way to cross them till I am there. That doesn't mean I must be discouraged by this, nor oblivious to these troubles...
On the other hand, I have read reports that said that is it possible and frequent hopping from one embassy to another, obtaining the needed visas for the following countries, not necessarily issued in your home country before the trip, then. For instance, the Myanmar arrangements could be done in Bangkok.
Knowing this, I will probably depart home 'only' with the visas for Belarus, Russia and China (not neccessary for Japan, Korea, Thailand, Georgia, and in Nepal, Armenia and Turkey issued at the border), so I'll try getting the ones for Mongolia and India in China, Vietnam, Laos, Cambodia and/or Myanmar in Thailand (there is a boat service from Yunnan to Thailand, with no Laos or Myanmar visas required), and so on. This will obviously lengthen the journey, but it is the only way to do it effectively.
I already wrote about the procedure to get the Russian and Belarussian visa, so the next step is the Chinese one. I am not sure about it yet; I will call the Chinese embassy to question several matters, like the advertised 'three months multiple entries' visa is easily granted and whether I could enter China from Nepal somehow (as an independent traveller or getting a tourist group, and its visa, right in Nepal).
Then Central Asia (Kyrgyzstan, Tajikistan, Uzbekistan, Turkmenistan and Azerbaijan) poses another challenge. If I could re-enter China from Nepal I will head North, West and then East up to the Kyrgyz border (hitch-hiking or hiring local drivers if public transportations are not available), but I have no idea what requirements are needed to get the visa for Kyrgyzstan. I would be able to ask about this in Urumqi, most probably, but then I won't know till I'll be there, again. I'm positive about Kyrgyzstan and I don't think it will be hard getting in, and then paying for the visas of Tajikistan and Uzbekistan there.
Turkmenistan is another matter: It has a reputation for being one of the more difficult to obtain. The hoops you'll need to jump through vary by nationality, but often involve needing to apply in person at their consulate in your home country, and letters of invitation from someone within Turkmenistan.
It is between Uzbekistan and Iran, so I will have to cross it (or take a plane out of there, which seems quite easy from Tashkent international airport, but not sure if there are flights to Iran, actually).
In case I gave up traversing Central Asia, my only way to Iran from India would be Pakistan (as quickly as I could), whose visa is easily obtained (in India?), apparently.
I am positive about Iran too and visas don't seem to be hard to obtain, but they're mostly issued at airports as I read:
In 2006 the rules for obtaining a tourist visa changed and it has become much easier for nationals of many countries to get in to Iran by obtaining a visa at the airport. Visa are issued at the Imam Khomeini and Mehrabad airports in Tehran, and also the airports at Mashad, Shiraz, Tabriz and Isfahan. The visa is valid for up to 17 days and costs US$50. You will receive the forms on arrival. Extending a tourist visa is very easy and can be done in most cities.
Anyway, I must remember to bring with me some passport-sized photos for all these visa forms!!