I admire your ideas to radically change the structure of the film, but many of the alterations will not work in the big picture. Moving 3PO's introduction to later leaves no room for dinner to be prepared as it were, and ends the scene very awkwardly. In this scenario we'd have "I'm Qui-Gon Jinn. Your son was kind enough to offer us shelter." BOOM, scene change. In it's original form it flows nicely into the 3PO scene; I don't think anything else could come after it and feel natural.
I don't know if I was the only person under this impression, but I thought we spent 3 days on Tatooine. Day 1: Arrival, Watto's, Sandstorm, Dinner. Day 2: Deal with Watto, Anakin finished racer. Day 3: Pod Race, Freedom, Departure. Notice when Qui-Gon goes back to Watto's shop it is in the middle of the day, and there is no trace of the sandstorm. I also always thought Obi-Wan contacts Qui-Gon about Sio Bibble's message at night, which is after dinner. Regardless if it was intended to be 2 days or 3, in this version it's going to be 3. Maul/Grievous will arrive after "Either way we're runnig out of time," confirming the night setting.
I'd be open to experimentation with moving the Qui-Gon/Shmi scene to Anakin leaving home, but I have my doubts as to whether it will flow. As for cutting Qui-Gon's bet for Anakin's freedom, again I understand what you're going for here but the way things are set up in the film this would make things extremely confusing. We would have no idea what Qui-Gon or Watto are talking about in their meeting after the pod race. And later when Qui-Gon explains he tried to free Shmi but Watto wouldn't have it, that's too much information to brush over and "reveal" later in the movie. The nauture of the film does not give itself to this delayed reveal.
The beats as I see them:
Anakin's Hovel
3PO
Gunray and Bibble
Dinner
Qui-Gon/Obi-Wan (Combine their communicator talks/more detial later)
Maul/Grievous Arrives (Probe Droids sprinkled in where they'll fit)
Deal With Watto
SOMETHING ELSE
Anakin Activates Racer
SOMETHING ELSE (I'm leaning towards cutting the Qui-Gon/Anakin night scene entirely, not just the midichlorine bits.)
Pod Hangar/"I'll take that bet."
Pod Race