Mobilize the Squardrons has:

Reaction: After you refresh, remove 1 focus token from a target objective or enhancement you control. 

Heavy Blaster Emplacement has:

Action: Focus this enhancement to have your opponent deal 1 damage to a unit he controls.

In the rulebook on page 30, the timing chart indicates there is an Action window before the end of the Refresh Phase ends.

Turn begins with Focus token on Heavy Blaster Emplacement, which gets removed during the second 'box' of the Refresh Phase. Can I use the Action on the Heavy Blaster Emplacement during the Action window specified in the Refresh Phase diagram and then after the Refresh Phase ends use the Reaction on Mobilize the Squadrons to remove the new Focus token, thus allowing me to effectively use the HBE twoce a turn?

My gut says yes, but the problem lies in page 12 of the rule book.  Refresh Phase, Step 1 has the text '(Any effect with the text "after you refresh" can be used after completing this step)'.  Somone who supposedly was a playtester says there will be an errata for this, that it's supposed to be at the end of the phase as you woudl expect.  And the card name escapes be, but it has a "After you refresh place one shield token…." which wouldn't work after step 1 because step 2 is remove shield tokens…..