Given the explicit wording on the upcoming Chopper astromech, and the fact that it doesn't include the phrase "up to your shield value", can you start ditching equipment right away, to build up extra shields on your ship?

Example:

• Horton Salm with Chopper, Twin Laser Turret, BTL-A4 Y-Wing, Bomb Loadout, and Guidance Chips (32)
• First & Second turn, slow-roll with a one straight or bank, and ditch the Loadout and G.Chips for 2 extra shields, giving you 5 total before the first engagement
• When you can't turn around to get a needed double-tap, eat the BTL-A4 title for another shield, unlocking your turret in the process

No. The phrase "up to your shield value" has been superfluous since the TFA Rules Reference included this line in its entry on "Shields" (p.17):

Quote

A ship cannot have more shield tokens that its shield value. If a ship has a number of shield tokens equal to its shield value, it cannot recover shields.

The rulebook. Answering questions that you may have!