There's no complete documentation on what the historical "tsubame-gaesh" technique is like, although there are stories here and there. Number 9 feels hard to translate into practice but not impossible.
I’ve successfully performed most of these variations except for #6, 7b, 7c or 8. I tried but failed on 6 and 8. I have not attempted #7b or 7c yet.
I’ve seen all of these pulled off successfully by at least one sensei or another (all but 9). I’ll have to find those videos on the web and link them in, if permitted.
There are several cutting techniques with this same name (no particular order):
1. Ryuseiken (complete form) -
a. Walking up to target, One-handed draw from sheath (nukitsuke) and kesa cut (left-to-right LtoR) near top of target
b. From waki-kamae (sword behind you on right side), cutting upwards / kiri-age / gyaku-kesa from RtoL low on the target
c. Before the cut portion of the goza falls off (floating), suihei (horizontal cut) from LtoR
d. Switch feet, and suihei from RtoL
e. Guard/zanshin, and back off
2. Ryuseiken (simpler variations) -
a. Similar to this but without the nukitsuke and second suihei; OR
b. Similar with only kiri-age and then kesa instead of suihei; OR
c. similar but just standing in front (no walking)
3. Nukitsuke - Cross-cut
a. Moving up to target, nukitsuke kiri-age from LtoR
b. Before cut portion falls off, one-handed (katatte) kesa-giri from LtoR - the two cuts look like an X
NOTE: A variation of this while standing before target.
4. Mizu(hi) Gaesh
a. Standing before target, kiri-age from LtoR
b. Before goza falls, suihei from RtoL
5. Toyama-ryu Tsubamegaesh (I may be wrong on this one)
a. Two targets on two stands –
b. Kesagiri on target on left
c. Before goza falls, immediately to kiriage on target on right
d. (Wide swing) Suihei across both targets
6. Variation #6 (I can’t find the name right now)
a. Kiri-age from RtoL
b. While floating, kiri-age again RtoL
NOTE: the version I’ve seen are two handed, but this could be done one-handed as well.
7. Ryusieken on multiple goza
a. Typically this is #2b with 2 goza lined in parallel (on a yokonarabi)
b. Same as 7a with 3 goza
c. #1 with 2 goza (note: nukitsuke kesa on 2 goza)
NOTE: Theoretically #1 with 3 or more goza is possible but I have yet to see anyone pull it off.
8. Any of the above with a double- or triple-rolled goza
a. There is a single target but 2 goza are wrapped together into that one target.
b. Same as 8a but with 3 or more goza
NOTE: Since these are thicker, they are more likely to “float” or even just on the target.
9. The historical anecdote I wrote in this post
which is a recollection of Sasaki Kojiro’s technique.