As a side note, p7 dot sparkers imply the existence of oscillators with periods 196+70N for all N >= 0, I believe. (P196 shown below, featuring what is probably the most difficult weld I've ever undertaken successfully:)

`x = 46, y = 55, rule = B3/S2-i34q`

12bo20bo$11bobo18bobo$10bobobo16bobobo$10bobobo16bobobo$8b2obobob2o12b

2obobob2o$8bo2bobo2bo12bo2bobo2bo$4b2o4bobobo4b2o4b2o4bobobo4b2o$3bo2b

o2b2o3b2o2bo2bo2bo2bo2b2o3b2o2bo2bo$4b2o2bo2b3o2bo2b2o4b2o2bo2b3o2bo2b

2o$6b2obo5bob2o8b2obo5bob2o$6bo2bob3obo2bo8bo2bob3obo2bo$4b2o2bobobob

obo2b2o4b2o2bobobobobo2b2o$5bob2o7b2obo3bo2bob2o7b2obo$5bo2bo2bobo2bo

2bo3b2obo2bo2bobo2bo2bo$6bobobobobobobo5bo2bobobobobobobo$2bo4bobobob

obobo4bobo3bobobobobobo4bo$2b3o4bo5bo4b3ob2o4bo5bo4b3o$2o3bo2bobobobo

bo2bo3bo2bo2bobobobobo2bo3b2o$o2b2o2bo2bobobo2bo2b2obobo2bo2bobobo2bo

2b2o2bo$b2obob2obob3obob2obobo2bob2obob3obob2obob2o$4bo2bobo2bo2bobo2b

o2b3o2bobo2bo2bobo2bo$4b2o13b2o5bo13b2o$8b2o5b2o6b3o3b2o5b2o$23bo$12b

o20bo2$12bobo$11bo2bo$12bobo2$12bo20bo$23bo$8b2o5b2o6b3o3b2o5b2o$4b2o

13b2o5bo13b2o$4bo2bobo2bo2bobo2bo2b3o2bobo2bo2bobo2bo$b2obob2obob3obo

b2obobo2bob2obob3obob2obob2o$o2b2o2bo2bobobo2bo2b2obobo2bo2bobobo2bo2b

2o2bo$2o3bo2bobobobobo2bo3bo2bo2bobobobobo2bo3b2o$2b3o4bo5bo4b3ob2o4b

o5bo4b3o$2bo4bobobobobobo4bobo3bobobobobobo4bo$6bobobobobobobo5bo2bob

obobobobobo$5bo2bo2bobo2bo2bo3b2obo2bo2bobo2bo2bo$5bob2o7b2obo3bo2bob

2o7b2obo$4b2o2bobobobobo2b2o4b2o2bobobobobo2b2o$6bo2bob3obo2bo8bo2bob

3obo2bo$6b2obo5bob2o8b2obo5bob2o$4b2o2bo2b3o2bo2b2o4b2o2bo2b3o2bo2b2o

$3bo2bo2b2o3b2o2bo2bo2bo2bo2b2o3b2o2bo2bo$4b2o4bobobo4b2o4b2o4bobobo4b

2o$8bo2bobo2bo12bo2bobo2bo$8b2obobob2o12b2obobob2o$10bobobo16bobobo$10b

obobo16bobobo$11bobo18bobo$12bo20bo!

Also, the symmetric extended 1c/2 has appeared several more times, and has overtaken the asymmetric version as the second-most-common period 2 ship. All occurrences so far form in pretty much the same way, though, so no new leads on an improved synthesis.

EDIT: I'm having trouble finding p7 domino sparkers, which is unfortunate but not as important as dot/thumb sparkers are due to the existence of T shuttles. Here's the longest partial I have so far:

`x = 20, y = 29, rule = B3/S2-i34q`

9b2o2$6bo6bo$6bo6bo$7b6o$6bo6bo3$9b2o$3b2o3bo2bo3b2o$3b2o2b2o2b2o2b2o

2$6bobo2bobo$4b5o2b5o$3bo4bo2bo4bo$4b12o$6bo2b2o2bo2$7b2o2b2o$6b2o4b2o

$5bobo4bobo$bo3bobo4bobo3bo$obo5bo2bo5bobo$obo6b2o6bobo$bob2o10b2obo$

3bo3bo4bo3bo$3bo3b6o3bo$4b2o8b2o$5bo8bo!

EDIT 2: 4G 2c/6:

`x = 0, y = 0, rule = B3/S2-i34q`

16$15bo$13bobo$14b2o8$39bobo$39b2o$40bo8$37b2o$27b3o7bobo$29bo7bo$28bo!

5G super^2 pond:

`x = 0, y = 0, rule = B3/S2-i34q`

19$42bobo$42b2o$19bobo21bo$20b2o$20bo14$27b3o7b2o$29bo7bobo$28bo8bo!

7G tripole with (probably) reducible cleanup:

`x = 48, y = 33, rule = B3/S2-i34q`

47bo$bo43b2o$2bo43b2o$3o7$40bobo$40b2o$bo33bo5bo$2bo32bobo$3o32b2o12$

16b3o$18bo$17bo2$26b2o$25b2o$27bo!

4G T eater:

`x = 0, y = 0, rule = B3/S2-i34q`

26$43bobo$43b2o$44bo5$34bo$33b2o$33bobo2$27b3o$29bo$28bo7$20b3o$22bo$21bo!

(All from stdin_WM_4G.)