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The OP's question was about the minimum focal length required and the discussion has wandered around this and its been interesting, but I cant help but think that the FL he needs is more likely constrained by the FL that the rest of his system can support.
Anyone who has imaged at long FL has discovered how much more exponentially worse all the problems become.
Things that werent even considerations become significant problems and obstacles.
Talking about 1 arc sec seeing or sub arc sec image scale becomes a moot point if the rest of the noise in your system is being measured in many 10's of arc secs or even arc minutes !
eg your mount has more Periodic error than a few arc secs and there is no PEC, if mount backlash exists and is a problem, if mount capacity is at its limit, mount's ability to hold stability with light breeze etc, if polar alignment is not perfect - eg under say 10 arc secs, if tracking is limited or if there is no tracking and pointing correction for example, if your guiding errors are more than an arc sec, if you can't hold focus across an imaging session, if guiding flexure or mirror flop is occurring . . . its a long list.
You simply cannot capture the theoretical image detail in your subs if the mechanical noise in your system exceeds the telecope spot size, image scale or the seeing.
If that noise greatly exceeds the theoretical limits then its a failed exercise.
So IMO the answer needs to at least consider as much about what the OP's existing system is capable of yielding, since the budget is only $2000 it doesnt allow for any other upgrades other than OTA.
So for example
What is the existing PE and backlash ?
What is a typical PA for this system and the methods used
What is the tracking and guiding providing now at low FL and how will that be affected by increasing FL etc.
The choice of camera and sub length is relevant too - if the minimum sky noise and read noise limited sub length is sufficiently long but the mounts ability to track accurately or remain focussed for that length of time is compromised then its going to be difficult to obtain good results.
Imaging at longer FL is a whole new ball game, the status quo is not the same as imaging at a forgiving 770mm on a small light weight scope at an image scale of around 1.5 as/p
Its all doable and encouragement given, but knowing what you are up against is an important consideration.
I've seen EQ6's (and I see this one is belt modded) that had well over 1 arc minute of mechanical error - backlash and PE
Even after hypertuning, relubing, swarf removal and bearing upgrades the errors were still in the 10's of arc secs.
My 2c worth
Cheers
Rally
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