All of my questions were regarding the tajik visa. Not the uzebk visa. Sorry if that wasn't clear, thought it was given the forum is about the tajik embassy in DC.
Sorry, my mistake.
A visa for your next country isn't required in order to get an Uzbek visa, especially since they have no fixed exit port (you could just tell them you're exiting to Kyrgyzstan, where you don't need a visa).
In the past the ZTDA has provided individuals with letters of invitation free of charge, but their website currently makes no mention of it.
https://www.tripadvisor.com/ShowTopic-g ... istan.html
http://www.ztda-tourism.tj/en/feedback/ ... ageId/448/
As for whether you actually need a LoI to get your visa from the DC embassy, it's probably best to email or call them for clarification. Their requirements on their website are a bit opaque. I'm not sure you will be able to get a GBAO permit from them, as my impression is many embassies outside Central Asia do not issue them. Perhaps doing your trip in reverse and starting in Bishkek will make things easier, as visa + GBAO is dead easy in Bishkek.