So I emailed several different companies that offer Russian LOIs, and asked why they only offer single. The unanimous answer was that Russian Federation does not allow tourist invitations to be longer than 30 days, and only allows single/double. But they all assure me that as an American I can get a multiple entry visa with only a 30 day single entry LOI. Basically the one English-speaking guy at the embassy doesn't know about this special rule for Americans and he is trying to follow every rule too closely. So I print out several of the emails, then I bought a highlighter pen (because the guy loves to use his highlighter to show the "mistakes", so I'll use his strategy against him) and highlighted the important parts. I also printed out the page from the Russia Embassy of USA website and highlighted this:
I. In accordance with the Agreement between the Russian Federation and the United States of America on the simplification of visa formalities for nationals of the Russian Federation and nationals of the United States of America, the US citizens shall as a rule be issued multiple-entry business, private, humanitarian and tourist visas that are valid for three years (36 months) from the date of issue of the visa.
IN THIS RESPECT – FOR THE PURPOSE OF THE FULL IMPLEMENTATION OF THE AGREEMENT ON THE SIMPLIFICATION OF VISA FORMALITIES - IT IS RECOMMENDED THAT US CITIZENS APPLY FOR THREE YEAR MULTIPLE-ENTRY BUSINESS, PRIVATE, HUMANITARIAN AND TOURIST VISAS REGARDLESS OF THE PERIOD OF STAY STATED IN THEIR INVITATIONS.
When filling out the electronic visa application form at: http://visa.kdmid.ru
please choose «multiple» from the drop-down menu and indicate a 3-year period of stay starting from the date of entry in your visa support documents (invitation).
After reading the emails he just said no, and he doesn't know anything about this. But after reading through the above letter a couple times, he said please wait and took the letter and my passport and left for several minutes. Then he came back and said that the Consul said that it is "OK".
But he isn't done trying to deny my application... he does an error-check over my documents, then he gets to my insurance papers, which I've bought to cover the dates of my LOI. Then he tells me that my insurance must be valid until 31 August 2021!!! It almost made me laugh, but I quickly told him that it is not possible to purchase insurance 3 years in advance, but that I will be sure to purchase again before my next entry. Now I will have my fingers crossed for the next 10 days, who knows what they will say about a brand new passport that doesn't even have a Georgian entry stamp.
As for the LOI, I purchased through Fortuna Travel. They offer a "multi-entry" option for $50 that now I think is a rip-off, but in my special case with this embassy, it seemed like the only option. They also offer for $12 a single entry LOI, which will be the same thing, except it doesn't have a small statement on the right side which says "valid for multiple entry Visa".
Also, I just found out that there is a brand new Russian visa service center that just opened in Tbilisi, just off of Rustaveli Ave, several blocks from Liberty Square, shows up on gmaps. It seems that they are just charging a service fee to assist with the documents and hopefully to bring them to the embassy for you (which might actually be worth the 30 Lari to avoid those crowds!). https://tass-georgia.ge/en/
Also, the best method I've found for fighting your way through the crowd is to approach fast and confidently, push/pull your way through with a sense of authority, maybe say "excuse me" in english, but the people standing right at the gate will hold usually not budge until the guards tell them to let someone in. So when you are close enough to make eye contact with one of the guards, show your foreign passport and say "Touristi Visa". Personally, I hate using this special privilage because of where I'm from, but otherwise you can stand out there for a solid hour and never get close enough to talk to a guard. And most of the people seem to be waiting for, well, I dont know because some never seem to get it.
After visiting the special interests building on 4 different occassions, I just have to chaulk it up to another unique cultural experience that you don't get many other places.