well, i apology cosmoe, but it is difficult to explain in whole how to counter. basically what you want to do does not work. the main point to counter is to not allow you snipe kills. play definsivey enough for that. it is possible and because reg cant hold a flag against any dg early on, the other dominate easaly at least 2 flags.
secondly some of the combos above allow double or tripple chain stun so if they coordinate right they kick your ub and oak out of the lane faster than reg can get to a snipe. what i basically want to say is that your sugested reg is one of the main weak-points. the second is the oak.
yes i know their advantages at some stages of the game. but as you are talking about best strategy for 3vs3 on cataract i assume also very good players playing together. take rook, ereb and ub - triple stun insta death. its still counterable but it is better than what you suggested.
having a sedna helps the other team to push 2vs2 ignoring the reg that is occupied not getting killed by the third dg. of course, a well played sedna with right skilling and itemization and an ub or ereb aside her. and really, if ub an OOZE ub not wasting any slots for mana items!
if it is to make the strongest combo i would never put reg and oak together in it, taling about 3on3. oak shines later, too late. reg... well depends on skilling. but how you suggest it you hope that you get early easy kills. good opponents just play a bit more defensive and deny you any snipe kill. after level 3 or so they can get quite aggrassib without fearing snipe anymore. and they didn't not need to give up war rank or exp. you dont need to hold the hp flag to gain lead.
well, i don't think my answer can satisfy you. it even does not satisfy me. its too much, too mayn details to write down. but briefly, i think it is a good strategy but quite far away from the best. i would not be scared, not a bit.
p.s. i play reg too, quite often and allways snipe and mine based. i more or less do what you suggested (even though the skilling is abit different) and it works most of the time. but only because people allways forget to count in the snipe. except for my bad moments i usually never die due to snipe attacks. but i saw too many people just hoping "maybe he does not se me, or forgot me, or has no mana for snipe....".
p.p.s. anyway. play that you will have fun i bet. its not about the best combo. you rarly meet the best coutner combo. its about fun and with your strategie you will have alot of fun in most cases, for sure! i like the idea. but i don't think its on the top of the best strategies/combos.
edit: i hope no one feels offended. its my opnion. aynbody may disagree wiith that as i often do with what others do/build/play. sometimes i am wrong, sometimes not. there are many ways to win and finally, the palyer makes the most difference, not the dg.