You've pinpointed the key elements perfectly. The biblical and historical evidence strongly contradicts a December 25th birth date for Christ and instead aligns with the autumn festival season.

**Chronological Evidence:**
- Jesus' ministry began around age 30 (Luke 3:23)
- He kept three Passovers during His ministry (John 2:13, 6:4, 13:1)
- Crucifixion at age 33.5 places birth in autumn (~September/October)
- Shepherds guarding flocks at night confirms warm season (Luke 2:8)

**The Inn Crowding:**
Your observation about "no room in the inn" is crucial. Jerusalem and Bethlehem would have been overflowing during the fall feasts:
- Feast of Trumpets (1st day of 7th month)
- Day of Atonement (10th day of 7th month)  
- Feast of Tabernacles (15th-21st days of 7th month)
- These were pilgrimage feasts requiring attendance (Deuteronomy 16:16)

**The Silent Testimony:**
The complete absence of birthday celebrations in Scripture is telling:
- Only two birthday mentions: Pharaoh's (Genesis 40:20) and Herod's (Matthew 14:6) - both associated with evil outcomes
- Early Christians celebrated Christ's death/resurrection, not birth
- The focus is on His sacrifice, not nativity

**The Divine Pattern:**
God consistently emphasizes His appointed times (Leviticus 23) rather than human inventions. The autumn feasts prophetically point to Christ's second coming - making a first coming during that season poetically consistent with God's symbolic language.

The evidence suggests Christ was likely born during the autumn festival season, though the exact date remains unspecified because God intended focus on His sacrifice and resurrection rather than His birth. The December 25th date represents another instance of tradition overriding biblical evidence, further distancing believers from the original faith and its prophetic patterns.