This method would be... contrary to lore.
During the chat with Yaroslev Tartakovsky in the hot labs, Shepard can inquire about the need for a male in reproduction. The reply indicates that queens contain all the needed genetic material from their fathers - which would imply that some other breeding pair is needed to create a royal egg.
The specifics of the Rachni's reproductive process is a little nebulous granted.
The wiki has this to say on their reproduction cycle:
Though queens are usually mated to brood warriors, the reproductive processes of the rachni do not necessarily require a male counterpart. Queens carry the genetic information of their fathers inside them, allowing them to lay eggs even if no brood warriors are present. They are said to be able to lay a massive amount of eggs every few hours, resulting in an entire rachni colony within days.
You are right in that a breeding pair is suggested, but if a Queen can propagate her species with her own offspring, there is no reason to believe that she would be unable to produce a viable royal egg. Even if the Queen requires a male Brood Warrior there is nothing stopping her from laying a few for the specific purpose of making new Queens. The lore doesn't specifically say how long a male Brood Warrior takes to reach maturity, but it does say that a queen can produce a colony of Rachni within days. Plus Shepard fights several fully grown Brood Warriors in ME 1, and they were only recently spawned by the Queen if we account for the time between the the newborn being separated from her and the loss of the Peak 15 facility.
If a Brood Warrior is needed for a royal egg, then the Queen would have from the time she is freed from Reaper control during the Genophage arc till the fall of Thessia (if we assume that is when the ark would leave) to mate with a male, which is more than enough time considering their gestation rate (IMO).
Some of the other cloning methods you mentioned might work, though. I might be a bit concerned about the source due to the genetic memory thing they share.
True, it would be problematic, but even if the resulting queen didn't share the original's penchant for co-operation, there is no reason to assume that she would be unwilling to work with the refugees. She could be appeased by the fact that these races did just resurrect her and save her from annihilation by the Reapers, and that by traveling into the unknown it would beneficial for both parties to work together.
Even if the procedure left this clone 'deranged' the ark personnel could still make use of her offspring by sending the insane drones down to a planet, waiting for them to establish a colony, and then sending the Krogan in to wipe them out. Free labor, and a perfectly suitable foundation for a colony, all in the span of a week or two.