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This program should do what you want:

function: push REROLL:s HITS:n SIXES:n {
 NEW_HITS: [count {5, 6} in REROLL]
 NEW_SIXES: [count 6 in REROLL]
 if SIXES + NEW_SIXES >= 2 {
  result: 3
 }
 if NEW_HITS >= 1 {
  result: [lowest of HITS + NEW_HITS and 2]
 }
 result: [lowest of HITS - 1 and 2]
}

function: vaesen INITIAL:s {
 HITS: [count {5, 6} in INITIAL]
 SIXES: [count 6 in INITIAL]
 BLANKS: [count {2, 3, 4} in INITIAL]
 if SIXES >= 2 {
  result: 3
 }
 if HITS >= 1 & BLANKS >= 1 {
  result: [push BLANKSd6 HITS SIXES]
 }
 result: [lowest of HITS and 2]
}

loop C over {1..6} {
 output [vaesen Cd6] named "[C]d"
}

Note that there are some subtleties:

• There is no reason to reroll if you rolled two sixes initially.
• You can't reroll if there are no blanks.

You might also explore strategic pushing.

For what it's worth, I have a more advanced calculator for the SRD version of the Year Zero Engine, though Vaesen does not use this version.