Brian: You're definitely getting to the issue of the question, or issues for that matter.
There continue to be quite alot of questions, as we've seen in one or more threads about how to treat new chips added to a prior bet not yet pulled in... this is a twist on that, as you correctly connect it to Rule 44.
Further, I'd bring attention to your point: I have seen and at the time took no issue with a player doing something along the lines of pulling the 500 back and throwing 200 back in and folding; based on the quickness of the maneuver I didn't judge any ill intent. . So that, yes, whether it's exactly kosher or not, players will from time to time straighten out their bets, whether calling or folding, and "based on the obvious intent and quickness", we often don't make a big point about it. For example, in the OP, the player might drop a couple 1000's while pulling back the 500, to leave a 3000 smooth call, obvious what he's doing and it speeds the game up.
But what happens when it's not such a smooth, obvious maneuver? Which is exactly what you picked up on....
You offer one solution for discussion: that silently retrieving a prior bet chip not yet pulled in should be ruled an intent to act (either calling or raising, but not folding).
...As a twist on that language, we could also look at: Players are discouraged from disturbing prior bet chips as this can be disruptive and raise questions as to the player's intent. In TD's sole discretion this may be interpreted as an intent to act, and may be subject to warning or penalty. Reason being that 1) we may not want an automatic trigger requiring a call or raise in every case, and 2) to make it clear that the TD can rule this as intent to act.
BIG ISSUE: Let's say the player pulls back a chip or chips, and tanks... and you decide to declare he must act... what happens if he verbally declares fold at that point?? Is that string action... same as saying "I call, I fold"... you accept the call but not the fold (until the call is made of course).... or ?
Many thanks for the ideas!