just seeing if anybody else does rundowns this way. we've done this for my 6 years as head coach on the high school level and have never botched one.
instead of going to the next bag to replace we replace ourselves.
for example if we have a pick at first the firstbaseman will make the first throw of the rundown and then go back to first. the pitcher would get the next throw at first and replace himself behind the firstbaseman after his throw. the 2nd baseman and ss would replace themselves at 2nd. we dont follow our throws.
we start everyyear saying we are going to do it the "right way" but end up executing this way much better.
does anybody else do this? it really works for us.

I do see less of a chance for obstruction your way.I have seen players throw and follow their throw and then not clear the running path as they passed the runner.

Interesting your way.

its different - and im definitely not saying its right - buts its been extremely effective/successful for us.

I got to say I pride myself in executing rundowns because we practice them as a get loose drill pretty much everyday in practice. We have even turned double plays in them before catching a runner trying to advance.

I don't teach it your way but I think I like it. It does help eliminate the possibility of interference calls.

What do you have the other players do while doing this in a game situation?

they do the same thing as normal - backing up - covering bags, etc. the same.
in a 1st and 3rd situation your leftfielder will become involved in any rundown at 3rd more than likely.
we teach our runners if they are in a rundown to find a player without the ball and run into them. this really cuts down on those possibilities.
like i said we havent botched a rundown since we started doing it this way.

I have taught it both ways in my young coaching career.

I always called those "2 circles" or "figure 8".

I taught 2 circles until I realized MLB uses mostly figure 8.